View Full Version : Topology & Geometry
- intro to differential forms
- differential geometry and tensor calculus
- tensor
- basic tools for quantized differential geometry
- A Toy Principle Bundle
- Comments on Toy Principle Bundle
- Differential forms. Why?
- Geometry with non-compact groups, e.g. Freidel/Livine
- Enveloping spaces
- Why no images?
- Proposed Resource Sticky for Quantum Differential Geometry
- Synge's Theorem
- [SOLVED] Euler 9 point circle
- Metrics and coordinate transforms
- Calculating an inertia tensor
- differential geometry lecture notes
- pushforward of Lie bracket
- Theorem between Curvature and submanifolds
- Question
- Groups in GR
- Another question
- Geodesic Deviation
- definition of a vector using transformations
- 4-volume is a rank (0,0) tensor?
- Help me out.
- Transform rule for (1,2) tensor
- What is a vector?
- Question on Topological Spaces
- Request for help and/or comments
- atlas
- How to start with Tensors
- Which of the following is a metric on S? d^2 or d^(1/2)
- Quick Introduction to Tensor Analysis
- Scalar Equations!
- Lie transport vs. parallel transport
- expanding manifold with constant boundary
- possible circlular answer...
- If curvature were an exact differential
- Twisted forms and intuition.
- Homogeneous points & coordinates
- tensor product
- Structure constant calculation
- Hodge numbers of 2n-dimensional torus
- Embedding a line into a plane
- Non-commutitative geometry
- The Four Vertex Theorem
- Isotopy in Topology
- Tangent/normal/area for this Circle..
- What is a Vector Bundle?
- Determinant of metric tensor
- Some basic problems in Riemannian Geometry
- What's a surface patch?
- Extrinsic/Intrinsic curvature
- Third Bianchi identity
- parallel lines and space curvature
- lecture notes discrete manifolds
- Diff operators are Covariant
- Math "Newb" Wants to know what a Tensor is
- Tensor identity - Help
- A monkey learning tensor
- what is a tensor
- Applications of tensors
- any idea on this
- diffeomorphism invariance
- intro tensors book
- Outsider question about DG
- Intersecting subspaces in N dimensions
- Christoffel symbol as tensor
- Lie algebra
- Directionality in Stokes Theorem for Volumes
- [MUST READ] This forum is not for homework or any textbook-style questions.
- Contravariant gradient?
- Harmonic curves
- Corses on differential geom
- algebric geometry
- Into troubles with a mesh
- 2nd Funadamental Form?
- showing scalars are unchanged by rotation
- tagent vector and vector field difference
- proof that grad V is a (1,1) tensor
- Most efficient backgrounder on differential geometry ?
- non-degenerate Poisson bracket and even-dimensional manifold
- Can someone help me solve these problems
- Klein Bottle
- Quotient space?
- i need to know how can i solve the following
- visualization of contangent vector?
- Continuous on a curve?
- Differential Geometry And Difference Geometry?
- Double Integral Volume
- corses on vector and principale bundles and spinorielle geometry
- geometric heat equation
- Solutions in differential forms
- about the basics of Poisson bracket
- Quotient topology
- Closure of an open ball and separable space?
- homotopy book
- differential forms question
- Best books for Differential Geometry?
- Transformation law for Christoffel symbol of first kind
- Prerequisites for Differential Geometry
- spherical geometry, some simple things
- covariant vs contravariant
- Differential Equations
- Intorduction to Lie Groups?
- equation of evolute?
- Spinor Decomposition of a tensor
- Tensors & Differential Geometry -- What are lie groups?
- The covariant derivative of a contravariant vector
- Rank 2 covariant tensors and dimesionality
- Stereographic projection
- Question On Homotopy Groups
- Unbounded space
- manifold question?
- Writing tensors in a different way?!
- cross product in higher dimensions?
- infinitie dimensions?
- Curl and a real set of data vectors
- A Geometric Approach to Differential Forms by David Bachman
- An extension of the concept of a tensor field
- Curve Evolution
- Extrinsic and Intrinsic Curvature
- curveture
- What is a tensor?
- Coordinate transformations
- Lie-derivative
- vectorfield
- Question on the properties of a manifold
- using surgeries to construct 4-manifolds of arbitrary topology
- lie groups-textbook
- Sunrises on the compass
- Hodge Duals and the Interior Product
- the curmufrence and the volume of a sphere...
- manifolds
- Extension of Thurston's Geometrization Conjecture to four dimensions?
- Quick question on Einstein Notation
- la direction d'un point
- Closed manifolds
- What is a tensor and why is it useful?
- Angle between space-like and time-like vectors
- Topology problem
- differential forms
- covariant derivative
- engineer becomes physicist? help me.
- Questions in topology/geometry
- Formula for non-linear differential forms
- Surface Transformation
- how to satisfy Laplace's equation ?
- Nonabelian gauge field
- Quick Diff Geometry question
- Got the theorem, having trouble with the proof...
- Question regarding tensors... derive acceleration in polar form
- Can you check my proof?
- flat torus embedding in euclidean space?
- Nakahara problems solutions
- Orientable Manifold with Boundary
- Topology problem No. 2
- matrices and tensors
- applied 3-sphere model
- Induced inner product
- funny definition of dimension of a topological space
- Linear Interpolation
- Rotated Spheroid
- Tensors
- vectors, one-forms and gradients
- Translation/Rotation
- Topology question?
- Deriving the Implicit Equation of a Rotated Spheroid
- Tensor analysis in curvilinear coordinates
- Finite Differences proving
- Good Texts for Independent Study
- riemann roch made easy
- DOFs in coordinate mapping if metrics specified?
- Kleinian view of geometry
- Bracketed subscripts
- [SOLVED] How to deduce rot and div formulas under spherical or cylinderical coordinat
- Help with basic tensor algebra
- How can i define "Hook's Law interm of Tensor"
- How to show something is a tensor.
- Atlas of manifold
- helix and radius of curvature
- tangent vectors
- Tringles on a sphere
- Euclidean Geometry Question
- What r the prerequisites for studying diff geo????
- manifolds
- maifold calculus
- Exterior differential
- Tensors and Topology
- Super Quick Question
- One-forms
- surface question (topology)
- Manifold Problems
- Symmetric Matrices and Manifolds Answer Guide
- Frobenius' Theorem
- The Poincare Conjecture.
- Open Subgroup of a Lie Group
- quadrupole-quadrupole interaction?
- projective plane as quotient space of a sphere
- Is an orthogonal transformation a tensor?
- The Geometric Heat Equation--WTF??
- Question about Alexander and Briggs notation
- Tensor emergency
- noncoordinate basis
- Homeomorphic Vs. Isotopic
- Physics and Topology
- definition of a smooth manifold.
- Lie Derivative of a One-Form
- Geometry - Stereographic projection
- A very special Möbius Strip
- What is the second fundamental form?
- Two quick questions on subspaces (intro to tensor calc)
- About curvature
- Contravariant derivative
- Torsion Tensor and Gauss Equation
- Qestion: Vector field and (n-1)-form representation of current density
- Tensors and Tensors
- Isotropic tensors
- tensor
- Worked Problems in Modern Differential Geometry
- Integral manifold
- Tangent bundle on the sphere
- Varying metric determinant
- tensor questions
- Euclidean and Non Euclidean Space?
- Inverse of the Stereographic Projection
- Introduction to Differential Geometry
- Isomorphic Tangent Spaces
- Acceleration Tensor - Rotating Frame
- GR and analytic continuation
- divergence of a tensor?
- properly discontinuous action of groups
- One-Forms
- Riemannian manifolds
- units?
- Homeomorphism
- Has anyone seen this scalar?
- optimization problem
- 4 dimensional spacetime manifold question
- Differential Forms vs. Directed Measures
- Who discovered the general case of Stokes' Theorem?
- why tensor analysis ???
- Various problems concerning Exterior calculus
- The Tensor Product
- Producing a Ricci tensor
- Differential Geometry/Ricci Calculus Question
- Proving an Identity from Differential Geometry
- Exterior derivative question
- MInimal surfaces...
- levi-civita permutation tensor, and kroneker delta
- Some geometry questions
- Lie algebra
- Schwarzschild Solution using Cartan's Formalism
- Question involving curvature tensor
- Stuck with basis for tangent space
- Conversion from Scalar Eq. to Vector Eq.
- the exterior derivitive 'd'
- Rank condition in the Implicit Mapping Theorm
- The Special Linear Group
- Geodesics in Minkowski Spacetime
- Covariant derivative of the gradient...
- Inverse function of a function of two variables
- Killing fields
- 1forms and Div, Curl, Grad
- Contracting.
- Exterior Derivative
- Riemannian volume form without local coordinates
- Reimann Geometry Resources
- differential of normal vector
- Textbook for General Relativity
- Lie group geometry, Clifford algebra, symmetric spaces, Kaluza-Klein, and all that
- Contitunity on a Manifold
- Convolution Theorem on Manifolds
- Basis vectors and covectors
- From Simple Groups to Quantum Field Theory
- Lie group, Riemannian metric, and connection
- Spivak's textbooks
- Evaluate a length on a quadric surface
- metric tensor on unit sphere
- structure constants of Lie algebra
- Musings on the physicists/mathematicians barrier
- Derivation Of The Faraday Two-Form
- Complete Solution of Poincare Conjecture
- Metric (distance Function)
- Lie group geometry
- What different between covariant metric tensor and contravariant metric tensor
- What is the metric tensor on a spherical surface?
- Why we have to definte covariant derivative?
- Weyl tensor
- Connections on fibre bundles
- Grisha got it!
- Quadlateration
- Fifith Postulate in Affine Spaces
- Ricci Tensor and Trace
- Riemannian Geometry
- "Discrete" Geommetry...
- 2-Sphere
- The Great Circle et al....
- Intro to tensors book for self-study?
- Coordinates in Riemannian Geometry
- Transforming to curved manifolds
- Question on homeomorfism
- Connected set and regular boundaries
- Meaning of integrating exterior forms
- Fundamenal Group
- Ricci and K (curvature)
- Cartan forms and structure equations
- I thought w(f) where w=dual vector f=vector is Reals?
- In which frame does the unit 2-sphere look locally flat?
- Curl of Tensor
- Tensors
- Question and answer on 'not exact' forms
- Spivak calculus on manifolds solutions? (someone asked this b4 and got ignored)
- Geodesic Curvature (Curvature of a curve)
- Notes
- Generalized Poisson brackets
- scalar, vector, mixed, etc products
- Cross product optimization
- dual space topology
- Book on tensor symmetry, geometries, surfaces
- Parallel Translation
- Complete riemannian metric
- How does a 2form act?
- Using Tensors in this Forum
- Gradients of Vectors and Dyadic Products
- Theorem of Curves in higher dimensions
- All isometries of the n-torus
- Definition of surface
- noncoordinate basis vector fields
- Transformations taking straight lines to straight lines
- Vector Fields and Vector Bundles
- principle bundles
- Surface area preserving flow
- wedge product property
- Inner product Pythagoras theorem
- Einstein notation stuff
- Hypersurfaces with vanishing extrinsic curvature
- Questions about Index Notation
- Mobius Strip? What's all the fuss about?
- Tangent space, derivation defifinition
- Differential Forms - Cartan
- Index transformation
- 4D surface
- Riemann
- learning tensors from scratch
- Tensor with complex eigenvalues
- My Solutions to "Tensors and Manifolds"
- Help on contraction...
- Decomposable forms
- Notation question
- Cartan's Identity
- Star Operator
- Kahler geometry and potentials
- Lagrange equations with constraints
- Covariant and Contravariant Rank-2 Tensors
- Help with a function on S^2
- Lie Derivatives
- tensor and wedge products
- linear transition maps on manifolds
- Definition of differentiability on a manifold
- Surface with prescribed metric
- Tensor Newbie trying to find Kolecki's rhythm
- Covariant derivative: an sign error in the book?
- What's the difference?
- Help needed - Equation of a wedge shaped plane!!
- good differential geometry book
- Question on Dirac Delta and functional derivatives
- Easy but interesting.
- Poincare conjecture.
- What is a compact space?
- Weyl Tensor
- Schaum's outline
- Metric tensor
- Question On Metric!!!
- Intuitively what's the difference between Lie Derivative and Covariant Derivative?
- Hypercylindrical Volume
- tensor product
- Lie dragging a vector around the ellipse
- the kronecker delta
- The tensor product and its motivation
- an ellipse question?
- gaussian geometry.
- basis
- metric/metric tensor?
- Recommendations for diff geom. textbook
- Differential Forms?
- differential geometry recommendations
- Projective spaces
- Above-Below test
- Simply Connected and Fundamental Group
- What is the boundary of a surface???
- semigeodesic parameterization...I am a little confused
- covariant derivative
- differential of lin. transformation between vector spaces
- Distance Function vs. Metric
- paralell transport
- Killing vector fields
- original motivation of differential geometry
- tensor products and tensor algebras
- christoffel symbols examples
- From Christoffel symbols to connection 1-forms
- Hermitian-Einstein connection ...
- What is the hypervolume?
- Vector or not vector?
- Geodesics and the Lagrangian.
- Any right equivariant automorphisms that aren't group left actions?
- Bivectors/Trivectors: How to imagine?
- Curvature and Laplacian
- Riemann-tensor
- How to relate a one form to a vector.
- Connection coefficients entering differential operators
- stokes theorem
- WHY there is no scalar equation for a line in three dimensions ???
- Curvilinear Unit Vectors
- exterior derivative
- lie derivative
- How to get the normal bivector to a surface??
- Permutations
- Inflectional geodesics ?
- exact sequence & meaning of a corollary?
- partitions of unity
- Bonnet Transformation
- Affine Geometry/Space
- Symmetric Tensors and Matrices
- Building invariants
- maxwell tarpits
- help with paper on gradient descent evolution of surfaces
- Gauge covariant derivative in curvilinear coordinates
- bilinear forms and wedge products
- Ricci tensor problem
- Switching d
- Spacetime metric?
- pullback of fibre bundle
- higher order tensor
- Curve with ever increasing radius
- tensor expression
- How to Prove contracted Bianchi Identity
- Slow roll parameters
- Again on concept of tensor
- Selberg formula for trace.
- Curvature for surfaces?
- Hello all my tensor questions
- Quick question on formula
- inverse of a 4th order tensor
- Simple questions about weyl rescaling/Conformal transfo
- How many coordinate charts does it take to cover a surface?
- Appolonius
- relation between Ricci and Riemann curvature tensor
- "Tensors & Manifolds," Wasserman
- Elementary Differential Geometry Questions
- Basis ambiguity
- introduction to tensor calculus and continuum mechanics
- Curl in arbitrary coordinates
- ndependent components
- Lie Groups
- tangent spaces and derivations
- Tensor in fractal dimensions
- a simple derivation involving the Hodge dual
- Generalized PDEs with an apparent contradiction
- Grassmann manifolds
- angle preserving transformations
- G-torsor
- Understanding tensor contraction
- Thurston Geometries
- About Scalars
- some questions about tensor
- time is scalar?
- Intro to tensor material - If you have time please...
- vector field vs vector function
- Physicists agree?
- adjoint representation
- Functional determinant
- One- parameter groups
- Probability Tensor and Ellipsoid
- lie derivative
- continuous function
- exterior product
- Smooth Charts on immersion image.
- What's a 0-form and what's not?
- Question of vocabulary
- first countability
- differential structures
- Lie algebra question
- Poisson's Identity
- Symmetric Matrices as Submfld. of M_n. Prelim
- taking a course in calculus on manifolds.
- Exact definition of differential forms
- Help with universal theorem of coefficients for homology
- Holonomy, SO(6), SU(3) and SU(4)
- Help with Lagrangian to Eulerian transformation
- Morse Index
- Problem book on manifolds
- Comprehensive intro to diff geometry by Spivak Vol2.
- immersions and embeddings
- Need help on tensor
- Tensors
- Christoffel symbols from definition or Lagrangian
- Tensor Field
- Local approximation with ellipsoid
- tensor product
- holomorphic projective connections
- Geometry as a branch of physics
- Contraction of a tensor
- Equations of motion for differential forms.
- Is this correct? (Tensor)
- Coordinate Transformation
- vector field
- differential form
- differential form
- Spivak volume 2
- Discreminent(Hessian)
- Identities for covariant derivative
- Geodesics
- Submersion btw R and S^1
- why are tangent vectors like this?
- symmetrizing and skew symmetrizing tensors
- tensor analysis text?
- non-degenerate tensors?
- Parallelizable Manifold
- induced maps on tensor spaces
- geodesic in a curved space
- Differential forms and divergence
- Synge's inequality
- isometric immersion
- convert the coordiates of one vector between 2 Cartesian system
- geodesic deviation equation
- Derived systems: inverse problem
- Connections?
- Some elementary geometry questions
- de Rham cohomology
- Operations on 2 vector fields?
- Tensors links or ebooks ?
- Lie Groups, Technical/Def.
- Exponential map
- Extending Vector Fields.
- Geodesics and Diffeomorphisms
- Surface with Ricci scalar equal to two
- non-integrable tangent distributions
- Curvature of a space curve?
- subjects for symplectic geometry?
- one parameter family of metrics
- Geodesic coordinates and tensor identities
- Rotate point on sphere to exactly 'cut sphere in half'
- Covectors
- Tensor Product
- Transformation of Rank 2 mixed tensor
- immersion
- Frenet-Serre Frames and circles.
- Gauss Curvature
- Lie derivative of a function
- Non-Orthogonality of Frames Del/Delx^i ; i=1,...n
- please help an ignorant mathematician
- lie groups as riemann manifolds
- About tensorial calculus
- Surface Tensors
- Please prove this
- Lie groups & manifolds
- Are there propagating charged waves admitted in Maxwell’s equations?
- Isometry sub-group of the gauge group & the center of structural group
- Spivak Calc on Manifolds, p.85
- Help on differentiation of tensor fields
- general helix
- topological continuity (a few questions).
- Differential topology basics
- Advisement on 4-manifolds: please suggest
- Intersection form. Please help with notation
- scalar or vector?
- manifold-coordinates..
- metrics.
- Diffeomorphic manifolds
- [SOLVED] Reference for sphere eversion
- curl or maxwell equations in higher dimensions
- Advice on complex analysis, Riemann surface & complex mappings.
- fibre bundles
- do these go through a 2-dim sphere?
- Normal space goes to Normal space.
- definition of a function by a metric.
- Path connected and connected.
- curvature, torsion problem
- compactness and continuity.
- dimension of a topological space
- Examples for seperation axioms.
- Serre Spectral Sequence. Motivation
- Pascal's Triangle for non-commutative?
- computing product spaces?
- open compacted topology.
- Affine Connection
- Pullback
- The space of continuous functions.
- Reimannian metric tensor g
- Relative Singular Homology
- from the metric to the CS
- Divergence of a two dimensional 3 order tensor
- Tensor product commutes with pullback?
- Dyadic?
- Exterior Calculus and Differential Forms?
- General solution to y = exp(c_i T_i)x?
- Some Basic Stuff
- Adjoint of functional derivative
- Hodge operator and adjoints
- Geometry problem
- Tangent vectors to a manifold
- Book on lie groups
- Kahler manifolds
- Covariant derivative of metric tensor
- Parallel transport in flat polar coordinates
- Elie Cartan's Papers
- Tangent vectors in affine spaces
- Homotopy and Fundemental Group.
- Classification Theorem of Surfaces
- Lie subalgebra and subspace
- How to prove a function is an isometry
- Manifolds / Lie Groups - confusing notation
- Quotient spaces on Lie algebras
- Meromorphic differential
- Differential modulo another differential
- differential forms and degree
- Scalar Product/Dot Product.
- reconciling differential forms' inner product of wedge with geometric algebra dot
- Number of zeros of (tangent) vector field on sphere
- spivak's dual space definition?
- Dirac delta in curved spacetime
- Pushing a geodesic
- hypersurfaces and induced connections.
- intrinsic extrinsic
- Power Map
- isotropy subgroup?
- isotropy subgroup?
- The mystery of geodesics .
- killing vector help
- Diagrammatic Notation
- Max. Torus in Lie Group
- Foliation, fibration, fiber bundle?
- Tensor action on Vectors.
- Electrical Conductivity Tensor
- Lagrangian of electrodynamics
- The set {A in GL(n;R) | det(A)>0} is homeomorphic to the set {A in GL(n;R) | det(A)<0
- Simple Topology Question
- Quotient map (A simple one).
- Integration/Differentiation on abstract spaces
- Parallelizability vs. hairy ball theorem
- Lindelof Space.
- How to find rotation parameter in sphere?
- Are vector bundles principal bundles?
- 4 dimensional pyramid.
- Differential Forms and Areas
- Does Every Coordinate System Admit Local Othornormal Basis Vectors
- Topology Question:Connected Components
- functions on manifolds
- Rotaion group
- Ring of functions over M
- Fractals Please!
- manifolds in hilbert space?
- coordinates adapted to two vector fields
- Intuition for Covariant derivative of a Tensor Field
- kissing numbers
- Isometry question.
- centrally symmetric.
- Penrose's diagrammatic notation
- Gaussian Curvature of (x^2+y^2+1)^-2
- Vector addition in cylindrical coordinates
- Definition of arc length on manifolds without parametrization
- normal one-forms
- Geodesic surface
- to see a tensor
- Visualizing left action of SO(3) on itself
- A few questions on manifolds.
- Covariance and Contravariance
- Question about basis of Lie algebra/tangent
- CW Complexes
- divergence of mixed II-order tensors
- Smash Products
- Homotopy Extension Property
- Simple connectivity and finite coverings
- immersion
- vanishing measure of a set with codimenon 2
- exterior covariant derivative
- from tensor to scalar
- Indices in differential geometry
- Tensor operations and properties
- Covariant vectors vs reciprocal vectors
- index to matrix form
- Equaivalent Statements?
- Connection between complex curves and homology classes
- Gradient in spherical coordinates
- Action of Einstein equations
- Orinetability questions.
- Total derivative
- Implementing Sard's theorem.
- Frechet distance between surfaces
- Conservative vector field; classification of derivative
- Conformal equivalence
- Integration on chains in Spivak's calculus on manifolds
- isometry and orbit dimensions
- Integrating a 2-form on a 2-cube
- Naive tensor question?
- degree of a map
- Simply Connected Question
- visualising calabi yau manifolds
- Formal definitions of cutting and pasting etc
- curved line w/o a plane
- Analogy between vectors and covectors
- 3 points make a plane?
- metric in a hyperbolic space?
- need help for cycloid
- A small rectangle on a large ball - distortion?
- College Euclidean Geometry
- topology on N
- comma notation in tensor expression?
- The universal property characterizing the quotient topology
- differential geometry
- Finding new major axis of ellipse after stretching along arbitrary axis
- Line bundles and parallel transport
- Basic point set topology question
- Trivial topology on an arbitrary set?
- fuzzy differential geometry?
- An obtuse triangle and its circumcenter
- Working with the inverses of composite functions
- Volume of cylinder with a 45 degree branch
- Get Polygon Side Length From Radius
- what are the 'closed geodesic' ?
- lie derivative problem/error
- Short question about Laplacians
- About Torsion
- Action of Clifford-elements on vectors & spinors
- Help for question below
- How it will be solved
- How it will be solved
- Connected components of a manifold
- Questions regarding function operations on sets.
- Smooth structures
- Dense and open sets in R^n.
- Ricci-Tensor from Riemann in higher dimensional flat space
- Simpley Connectedness.
- Diff. Geometry Question
- Nontriviality of the Möbius bundle without orientability
- Trilateration work around
- Is the product of two open sets open?
- Banach space C(X)
- Another implememntation of van Kampen thoerem.
- Geometry Question
- Geometry proofs
- Conic sections over C[x,y]
- Adjuction Formula: Ideal sheafs and tensor products
- Rotations in Complex Plane
- Banach Space that is NOT Hilbert
- Topological transform of singular points?
- Why is the cusp not a submanifold?
- Do trapezium angles have to equal 360 degrees?
- "Easiest" topology textbook/book
- a question of the complete metric space!
- Signed angle between two 3D vectors
- Projective Space
- why is noise always gaussian?
- Space filling curves: two and a half questions
- Elementary questions about fibre bundles
- How can a highschool student study the nonuclidean geometry himself ?
- Tesseracts as building blocks?
- Rotating a circle around its x-axis
- Something I read somewhere about Spin manifolds, I don't remember where?
- compact Hausdorff space
- Degree of a Map
- differential geometry in quantum mechanics - conserved quantities
- Area section of a sphere used for integration?
- What is Spectral Geometry ??
- Normal form of a mobius transformation
- Naturality of the Lie bracket
- Tangent space question.
- Area between two eccentric circles
- stereographic projection
- Help with a special kind of Torus
- Hello! How to prove the min function is continuous?
- Topology - prerequisites
- Symmetry of distribution
- isometries and constants of motion
- Tensor indicies switch
- partitions of unity: support of a function
- Group action and a topological continuous mapping
- Rotation of spherical vectors
- Fractals - recommended texts
- Sphere in Spherical Coordinates
- Changing to x,y,z
- Closed or Open?
- The topology of rational numbers: connected sets
- representations of the lorentz group
- Curvature of curve with arbitrary parametrization
- Find the center of the curve in 3D made by 4-points
- Transformations involving singular points
- "Usual metric"
- Definition of a one-form
- A problem about integral curves on a manifold
- Newtonian mechanics on curved spacetime
- Trace of a tensor product
- Compatibility of the horizontality condition with the Bianchi identities
- This is clearly symmetric!
- Connection between Lie-Brackets an Embeddings
- question about differentiable structures
- wishing to learn more geometry
- General Relationship Between Area & Perimeter
- Question- abstract index notation
- Distances between samples in high dimensions. Curse of dimensions?
- sample topologies
- separable and normal topologies...
- Torsion, affine development and Levi-Civita connection
- Simple question about definition of tangent bundle
- A question on noncommutative geometry
- Circles in Non-Euclidean Geometry
- Counting the possible number of shapes.
- cup product structure of the n-torus
- Lie derivative of vector field = commutator
- Finding the co-ordinates of the points on a triangle
- Simple question about SU(2) and SO(3)
- dense geodesic
- How does a fibre bundle differ from base space X typical fibre?
- S^n not a mapping cylinder. S^n and homeom. subspaces
- Riemannian Connections: Summary
- 3D rays
- Dyadic Product and Index of Refraction
- how long would it take to read euclid's elements?
- de Rham theorem....
- Plotting the Mandelbrot set
- Tensor question about Hypersurfaces
- group
- Incomplete and completion
- Differentiation on Smooth Manifolds without Metric
- Triangular obelisk
- one-parameter family of metrics
- Sequential compactness
- Employment areas with PhD in Pure Maths??
- integrating the minimum metric
- Tensor components of a Hodge dual
- Number of different conics in a projective plane
- hereditarily normal, mutually separated subsets
- discrete topology, product topology
- Lexicographic Square, topology
- Creating a sphere from a spline curve
- Help with Convex.
- Please help to Find coordinates of a point formula Angle,Distance & first point known
- Dot, Scalar, Inner Product Question
- Sighting points on a sphere
- constructible sets contain a dense open subset of their closure
- Question on a simple geometry subject.
- Focus of an ellipse vs. cone
- Unable to understand the symbols....!!!
- Functions
- weak topology
- What is Holomorphic factorization?
- Help with triangle
- Defining scalar product from norm
- Computing inner products?
- Genericity of Uniquness of a Solution to a System with Non-Linear Equations
- a great circle is geodesic
- geodesic triangle
- Total boundedness in R^n
- differential geometry
- Co-ordinate Geometry
- Gaussian curvature
- Question about Milnor's topology fromthe diffable viewpoint
- Laplace on Grassmannian (N-1,N)
- Measures and alternating multilinear forms
- Divergence defined from volume element
- Parabolic Curve
- I have a conjecture/ possibly already a theorem
- Covariant derivative repect to connection?
- Stereographic Projection for "general" surfaces
- parabolic coordinates
- sphere, torus, degree, cohomology
- discrete math - equivalence relation
- representations of GL(2) on tensor products
- Michael Spivak
- Christofle symbol and determinant of metric tensor
- Orthogonal Transformation and condition
- find the coordinates of the point on the ellipsoid where the major axis meet
- What geometric applications do prime numbers have?
- Need 3-ball to 3-sphere projection equation
- Is there a standard for the definition of the wedge product?
- Couple of questions on linear geometry
- killing spinors
- Basis for tangent space and cotangent space
- weak topology on L^2 loop space
- homeomorphism of the projective n-space
- compatible metrics?
- Problem with Ricci tensor formula I cannot prove
- Surface integral with differential forms
- Submersion
- Calculating no. of polyhexagon
- closed subset (with respect to weak topology)?
- Warm thing about convex hulls
- coordinates of a point that touches the ellipsoid
- Defining the term "connected"
- Topology: Filter problem
- Ricci Tensor
- Construction of the Tensor Product
- simplifying a tensor expression
- Euclidian Proof
- Determine vertical height of a geometry
- Introduction to Topology
- Intrinsic curvature.
- hyperbolic geometry
- Exterior derivatives on fibre bundles
- Diffeomorphism
- can sets be bounded by infinity?
- How to say a given space is a manifold?
- Arclength on a PseudoRiemann Manifold
- Deceiving Simple Geometry Question
- Betti number
- Power Set
- injective and surjective
- preserves inclusions, unions intersections...
- injectivity vs. surjectivity
- How does a hemisphere differ from a disk?
- Q on Riemann domains
- Q on Riemann domains, revised
- Basic question regarding continuous inverses
- example of a non-integrable function f , such that |f| and f^2 are integrable?
- Vectors As Geometric Objects And Reciprocal Basis?
- mathematics descriptions of objects not found in the real world
- Intro to Diff. Geom. PLEASE COMMENT.
- Cylinder: Ratio Volume/Surface Area
- Intersection Form in 4-D. Followup.
- Basic Alg. Geometry: Nodal Singularities. Attn Wonk.
- Rudimentary tensor question
- Can the sum of angles of a planar triangle be greater than 180??
- comparing topologies
- subspace vs. subset
- Topologies Finer vs. Coarser
- open map
- Countable collection
- Subbasis vs. basis
- Curl of a vector in a NON-orthogonal curvilinear coordinate system
- Stiefel-Whiney Homology Classes
- About the coherent topology wiki page
- are of a circle segment
- Regions in complete graph
- Complex Polygon Detection
- What are examples of cellular decomposition?
- 3-D vector interpolation
- topological vector spaces
- How to show completeness of C(K)?
- union of intersections
- Three things I don't get about CW-complexes
- Exact Sequences
- Localizing a point in a circle by 2 points on the circumference
- Equation of Ellipse
- diffeomorphism vs. homeomorphism
- Closed but infinite space?
- Lie derivation and flows
- Christoffel symbols
- Geometry in *COMPLEX* spaces
- Introductory differential geometry text
- radii of curvature for pseudosphere
- topology continuity
- showing F is not continuous
- Convex Subsets of Topological Vector Spaces
- Closure and completeness
- symmetrized complex space
- orthonormal tetrad/frame name question
- Vector Fields on S^2, 0 only at 1 point.
- Change of Coordinate for V.Field in Mfld.
- Homotopies between circles and paths in the annulus {z: 0<a<|z|<b }
- Special Conformal Transformations
- How/why is the angle that substends an arc is equal to S/R (S=arc length, R=radius)?
- Similar triangles formed by the diagonals of a quadrilateral inscribed in a circle
- Metric Spaces
- convergence on R->R
- A Confusion about open sets
- Homology question
- differentiable structure
- Manifold with Boundary
- basis topology
- Help on volume
- Functional Analysis (Big Rudin)
- Open subspace of a compact space
- How do you get the Klein Bottle from two Möbius Strips?
- Homology of spheres from the M-V sequence
- calc height of cone with only volume and angle
- Orientations of curves and diffeomorphism
- Homology of the Klein Bottle using M-V sequences
- distance of a great circle
- How to encode direction information?
- Two questions about degree
- Regular values of immersion.
- Inverse of tensor using Einstein notation
- open sets in metric spaces
- Bundles and global sections, triviality.
- Induced Orientation on Mfld. Boundary.
- rotations and reflections
- Defining the integral of 1-forms without parametrization
- inclusions of submflds. and diffeomorphisms.
- Compactification and Extension of maps.
- Handles and non-orientible 3D manifolds
- Question of algebraic flavor in algebraic topolgy
- What is the next number in the sequence?
- About the definition of local degree
- Homology of Hawaiian Earrings
- Surface representative of homology class.
- Algebraic Topology
- Basic open cover
- Homology of S^n x R
- How to get the coordinates inside
- Excision
- Pereleman's Proof.
- topological group
- normal subgroup; topological group
- topological groups
- Invariance of Domain
- Topological representations of energy.
- Surface divergence of an order 2, rank 3 tensor
- surfaces of cubes & spheres
- algebraic topology, groups and covering short, exact sequences
- Formula for Area of Overlapping Rings?
- Best high-level introduction to classic geometry?
- Algebra question in algebraic topology
- exterior derivative/interior product/exterior derivative
- Formation Of A Helix
- How are these two proofs for the compactness of [a,b] equivalent?
- Another algebra question in algebraic topology
- Iterated Function Sequences Accumulation: Help!
- Classification of Vector Bundles over Spheres
- Trivial Tangent Bundles
- solved
- Stereographic projections of Laplace Transforms
- Trouble understanding derivation of covariant derivative
- can curves be parallel to each other？
- Rotating Shapes (2D C++)
- Homology of a connected sum
- Image reflected from cone interior with r=h
- Mathematical Definition of Tensor?
- adjoint boundary operator
- Curvature form of Cartan connections
- Expand cylinder to a surface
- Why is the tangent space of a lie group manifold at the origin the lie algebra?
- Alexander-Whiteney duality
- Riemann Curvature Tensor
- Coordinate transformation of contravariant vectors.
- Parallel transport analog of Stoke's theorem
- Lorentzian structure
- Sudden confusion about definitions of singular homology
- Conformal Killing vectors
- Position vector and tangent vector in Riemannian spaces
- Curvilinear Coordinates
- prove volume of a torus equation
- volume for a contour map
- About projection
- attaching maps in a product of CW-complexes
- How to find a trivialization of a torus
- Help!A problem about embedded surface.
- Cohomology = invariant forms
- Invariant forms on gl(n)
- Coordinates in hyperbolic geometry?
- Characterization of paracompactness
- simplicial homology
- Degree of multiplication map of a topological group
- Understanding nets
- Geometry- circles
- Why can the affinity connection be arbituarily chosen?
- Tangent vectors as derivations
- Volume of a spherical segment
- Surface like helicoid in S^3?
- free homotopy
- Is the rotation angle in Minkowski's diagram real or imaginary?
- umbilic points
- a maximally symmetric space
- inverse of continuous bijection
- Covering spaces of RP^n x RP^n
- A Monotone Test problem
- Two torus identification problems
- Textbooks on Fractals and Chaos
- Covariant Derivatives
- Tensor analysis text
- Geometry in spherical coordinate
- 'Distance' between MANY points ??
- Zero/One-dimensional rotation
- Geometry drawing environment
- tensors in Gemotric Algebra
- Lie derivatives and pullbacks
- Question about topological manifolds
- Trisecting angles in an alternate topology
- 2 big squares
- Contraction distributive property in GA
- Is there exist a shortest closed curve in the homology class of a simple closed curve
- Transformation
- Submersion and fiber bundles
- "push-forward" ?
- lemniscate locus
- 1+1=2
- How should the radius MP be drawn?
- drawing circles
- Circle inscribed in a circle.
- Homotopy Question
- Curvilinear Coordinates in Geometric Algebra?
- diffeomorphism
- Tensor notation
- Flattening metric tensor
- Representations of the Fundamental Group
- Non-Euclidean/Hyperbolic Geometry
- Euler number
- Great Circle question
- angle x
- Point on circle about square
- Weak and weak* convergence
- Cartesian coordinates vs. The rest of the world?
- How is (0,1) not compact?
- Tesseract
- Structure constants of a group antisymmetric?
- find the point which lie in a 3d line.
- Connected Metric Space Question
- Point inside a cube of irregular dimesnion
- Billiard Problem
- Holonomy of compact Ricci-flat Kaehler manifold
- Vanishing first betti number of kaehler manifold with global SU(m) holonomy
- Small slope approximation
- Normed and topological vector spaces
- Mapping with change of variable
- Helical path
- confused by open sets
- Exponential map of a lie group
- Challenging Problem!!! (Equivalent Metrics)
- Matrix Banach Space
- Two intersecting planes
- Vector Analysis Resources
- least upper bound
- what do you call a surface..
- Tensor notation
- RP^n as a topological space
- Families of "shapes"
- high school geometry book
- Problem on seperable banach spaces
- antisymmetrisation
- Is a mixed second rank tensor reducible?
- Lie theory question
- Linear Algebra Question in a Complex Geometry Proof
- How To Find Sides Of Right Triangle With Known Angles And Area?
- Geometry - The area and the goat
- Connected sum of topological manifolds
- Geodesic in plane when metric depends on single variable?
- Intuition behind compactness
- Isn't the circle connected?
- can i find such a metric?
- Limit Point of a Set
- Example of a covering set
- Another manifold definition deficiency?
- Prove that the bth projection map is continuous and open.
- Tensor integration
- Topology proof
- Bruhat-Tits Space
- Sphere question
- Projective Geometry question.
- characteristic classes of finite group representations
- wild metric on the 2 disc
- the kelin bottle and the projective plane
- Convergent Filter Base and Continuous Function
- For professionals - differential geometry
- Are there operators that change the curvature of manifolds?
- Product space
- Edwin Spanier Algebraic Topology difficulty?
- Covariant derivative in polar coordinates
- 4-Manifolds and Kirby Calculus by Gompf.
- DG vs. PDE course
- Geodesic deviation & Jacobi Equation
- Differential Topology
- Area of hyperbolic triangle
- Finding middle group in short exact sequence
- 16 different spherical coordinate systems
- Am I right?
- Basis
- discrete metric
- subracting dimensions
- Standard function topology?
- Topological proof of inifinitude of primes
- Curl of - \frac{1}{\rho} \vec \nabla p
- misunderstanding of isomorphism and automorphism
- Joint Gaussian With Tensors
- A Proof of Euler Theorem
- C^2 vs R^4 question
- Output a geometry rather than a number
- Maximal Exterior product of Tangent space
- Covariant vs contravariant
- deSitter Dimensions
- Levi-Civita connection
- Levi-Civita connection
- Aliasing riemannian geometry
- topological invariant integrals
- pushout of simplicial sets
- Local invariants
- basic method of finding geographic centre of a small country
- Orthonormal frame
- cubular homology cup product
- Curvatures
- compact -> hausdorff
- Subbasis
- light cone
- Geometrical meaning of spectrum in algebraic geometry
- smooth section in principal bundle
- Help with Frenet-Serret formula
- ε-Neighborhood
- theorem
- Improve Spatial Representation
- Origin translation tensor
- Levi-Civita Tensor Video
- smaller cross section of a closed surface
- Metric tensor and connection
- Scaling and Translation Invariance
- conjecture
- Lie Algebra of S3
- positioning points inside a triangle
- CW structure of S^m x S^n
- computing tangent spaces of implicitly defined manifolds
- Distance function
- Integral curves and one-parameter groups of diffeomorphisms
- Isomorphism between spaces
- Prove this Metric Space
- RP2 into R4 embedding
- n-sphere and its equator
- dot product of vector function?
- 3D Plot of a constrained function
- a commutative diagram
- Algebraic Geometry and Differential Equations
- Curvature and locally flat spaces
- divergence theorem
- curvilinear coordinates question
- two fold coverings
- Squaring the triangle
- open book
- Homology groups from Homotopy groups
- Poincare' disc
- flat world
- Proving that the cartesian metric is rotation invariant
- Nonsqueezing theorem - a proof with the action
- How to compute the cohomology of the Klein bottle
- Can someone explain this proof to me?
- how to prove there is no Lebesgue number for open cover (1/n,1)?
- relating inverse metric to densitized triads
- Composition of a Tricolorable knot
- how to find 3D point on the 3D line with given distance and from given 3D point
- KAM theory
- dyad product
- Rotating frames of Motion in Vector Notation
- How to compute the metric without an embedding
- sO(n) actions on vector bundles
- Geometry Proof. Help!!!
- LaTeX Q
- Complete set of answers to Schaum's Tensor Calculus
- Geometry Proof
- gluing maps from vector fields
- Moment Map
- Parallax, angle to observer etc.
- Visualizing Immersions vs. Submersions
- Differential geometry and hamiltonian dynamics
- euclidian topology ang cofinite topology
- Alexander duality
- Compass and straightedge angle construction
- Fundamental Group of the projective plane after we remove n points?
- Union of a pair of Atlases
- Non-symplectic flow
- Cone: solid or surface?
- Non 2nd-countable, Hausdorff, differentiable n-manifold?
- question whether 2 spaces are diffeomorphic
- Computating the components of a tensor
- Geometry Area Proof (quadrilateral)
- differentiable manifold not riemannian
- Tensor problem
- Lie groups, Affine Connections
- Solid Geometry
- Bivectors, Cartan Geometry and Curvature
- Properties of a volume in 3D Euclidean space
- Interesting geometry book?
- Orthogonal Transformations
- Trying to get my head around tangent bundles
- Algebraic geometry
- Algebraic Geometry (2nd question)
- Fundamental Group
- Help needed in understanding typology
- Trivial fundemental group
- Metric
- Apollonian Packing of Circles
- Perspective and Altitude
- alpha vs theta
- Local path connectedness
- corollary
- graphing complex function
- Trouble with simple example for Lie Derivative
- Matrix Formalism of Differential Geometry
- Regular spaces
- Gradient and differential notation
- Image of a curve
- Geometry of a conformal disk
- dimension of vector space
- Fundemental group, Torus, SVK
- Annoying principal bundle problem
- Helix along a helix
- Is an associated bundle isomorphic to the principal bundle?
- Question in topology
- problem in Algebraic Topology
- Forms on the circle
- Manifold: what's the meaning of this name?
- algebraic geometry
- Length of a portion of a circle
- Poincaré-Hopf Theorem
- Relationship between Chern and Levi-Civita Connections on Kahler Manifolds
- Advanced Algebraic Curves problem
- connectedness of the closed interval
- Coordinate chart
- help with 2 problems about compact/pointwise convergence from Munkres - Topology
- Building a Klein Bottle
- what algebraic space does a pseudotensor inhabit?
- Differential forms problem
- Algebraic topology textbook
- Closure of an abelian subgroup
- Modern Geometry
- Linear Spaces
- orthogonal projection of 2 points onto a plane
- Properties of adjacency matrix of graph with cycle
- Finding the sides of a right spherical triangle
- Geodesic equations
- Why is pi = circumference / diameter ?
- Representing a point in an n-dimensional space in a 2D geometrical shape
- Does an N-Cube have Surface Area?
- making a 3D pentagram
- easy question :)
- Curl of the transpose of a gradient of a vector: demonstration of an identity
- geodesics in non-smooth manifolds
- open set is countable union of disjoint open balls
- Topological Definition of Arc Length
- Total and exterior derivative of a 1-form
- Embedding manifolds that are not very flat.
- Proving Completeness of a function space
- Homology and Homotopy groups from properties
- Euler angles of rotation about x=y=z
- curvilinear coordinates question
- Measuring distances: why the Pythagoras formula
- Any good problem book on General Topology
- Conformally flat manifolds
- complex curvilinear coordinates(?)
- Distances, compactification & Möbius transformations
- 3D space where circumfernce = 4*pi*R
- Shape Operator vs Ricci curvature
- curved space
- difference between densities and n-forms?
- connected spaces in topology
- Torsion and homology: examples
- Angles on a Sphere
- matrices as topological spaces
- Lie group and Lie algebra
- Möbius transformations and SO(3)
- Diagrams of topological terms
- lateral edges of a pyramid
- Projecting the Earth...
- Homotopy (circle and line)
- good books of fiber bundles
- Closed/Open Transition Function Question
- Isometries Proofs
- Covariant derivative
- Fields and their relation to Tensors
- d-dimensional vs. n-dimensional ??
- Review High School level Geometry
- Affine Coordinate Ring question
- Connected vs. Path Connected Sets
- Ａ sine curve coiled in a sinusoidal fashion?
- what's the questions asking me to show?
- Topology Open and Closed Sets
- Question on page 7 Flander's book on differential forms
- Gradient Tensor of a vector field
- Proof of euclidean distance
- Use 3D lattice and vector field(s) to represent curved manifold?
- Need a bit more information about second-order tensors
- nuclear operators and trace
- Mass Point Geometry
- Witch of Agnesi
- a differential geometry question
- Osculating Planes
- Sphere Intersects with Plane
- Topology for Math GRE
- Arclength of a super helix?
- Knots: Simple Closed Polygons are Trivial, there are no quadrilateral, pentagon knots
- differential geometry : paramterization of an absolute value function
- curvature tensor of sphere radius R
- linking of curves
- Fundamental Group
- linked homotopy
- Make my own space
- circle x sphere = ???
- Intersection of simply connected
- differential geometry - strange formula
- polar coordinates: derivation from rotation group
- Christoffel simbol and derivative from him
- Showing that some curve is a circle
- parametrization vs. coordinate system
- about scalar curvature
- Relation between all 10 distance of 5 points
- length of parallel curve
- Extrinsic intrinsic
- Tensor of type (k,l)
- Geodesics
- how to represent a parametric curve?
- P-adic metric Strong triangle inequality
- combinatorics
- lie derivative clarification
- 2pier
- Metrics and metric tensors
- Simple Topology problem (Munkres)
- Affine parameter
- R^2 - A, with A being a countable set, path-connected?
- Fundamental Group of Matrices
- Integration of acceleration signal response data to obtain displacement rseponse data
- Determining 4-vector character of a 4-tuple
- Distinction between this geometric example of a Diffeomorphism & a Homeomorphism
- Nowhere dense subset of a metric space
- Geometric realization of topology
- Tensor Applications
- Modelling vehicle kinematic behaviour
- The VERY, VERY general equation of an ellipsoid - Who knows it?
- Geodesic and the shortest path
- A differential geometry question.
- simple topology question
- tensor derivative in continuum mechanics
- Equivalence relations and equivalence classes
- Wada basins
- geometric interpretation of a given Alexandrov compactification
- Identification Space
- how is 0-cell is a vertex
- Non-Riemannian Geommetry ??
- Deformation retract
- contraction map of geometric mean
- Mobius Band as Bundle Over S^1: Trivialization Containing (1,0) in S^1
- Adjoint of the scalar Lie derivative?
- connected component
- Closed using seq. criterion
- combinatorial problem
- Product of Two Metric Spaces
- Closed characteristics, closed orbits, periodic orbits
- Why is the boundary of the rationals (Q) equal to R?
- different metrics... same topology????
- Poincare conjecture
- Does trivial cotangent bundle implies trivial tangent bundle?
- Continuous functions in metric spaces
- What are the prerequisites for topology?
- interpretation of the covariant derivative
- Reflection/Rotation
- unbounded sets
- Why do you need a convex/concave function to do a Legendre transform?
- Stirling's formula?
- vector field
- Do I need ODE and PDE for differential topology?
- EINSTEIN Summation notation
- Can a sphere have flat geometry?
- Finding angles in a four sided room
- the lie bracket.
- Looking for a higher dimensional geometry book
- Affine plane
- Functional analysis and diff. forms
- Filling different shaped volumes
- Number of "independent" subcubes of a hypercube
- Homoclinic orbit?
- Funndamental Groups
- Identifying a Polyhedron
- linear maps
- Divergence Theorem on Manifolds
- Why is x > 0 not an open interval?
- Question on compactification
- Lie Derivatives
- Millenium Prize Problem solved!
- How many different topologies can X have?
- What is a nontrivial ultranet?
- Does a faithful action of SO(3) imply a metric on R^3?
- How to make curved line into torus?
- Elliptic functions and Poncelet's Porism together
- homeomorphism (defining a chart)
- vector field
- Please helppppp
- Composition
- definition of a manifold
- Brouwer's Fixed Point Theorem for Arbitrary Intervals
- Definition of a line between two points on a sphere
- metric coressponding to a set of curves?
- distance between 2 pullies
- cos(x) is not closed function?
- non-equivalent metrics on R^2
- Definition of the Cross Product?
- Central extensions
- sphere as an embedded submanifold
- residue calculus and gauss bonnet surfaces
- Contractible spaces
- A sequence or a single point?
- conic projection of a sphere
- Symplectic Manifolds
- geometric description of (simplicial)homologous cycles
- Represntative Surfaces/Curves in homology. Examples.?
- Need assistance,can you imagine a continuously deformation between X and Y?
- Square root loop
- external angle dilemna
- The coordinate ring - Algebraic geometry
- the FCT revisited
- Orientability of Complex Manifolds.
- 3D arc bounding box
- Connected Spaces
- Hyperbolic Geometry
- Relation between Frenet-Serret torsion and the torsion tensor?
- levi-civita connection assumptions
- An intuitive explanation to the Killing equation?
- For M a 4-mfld., every class in H_2(M;Z) can be represented by a Surface.
- When to use open/closed set,etc
- "Identifying" tiles in hyperbolic space?
- shortest arc between two points in polar coordinates
- pointwise multiplication as Hilbert-Schmidt operator on L^2
- Tangent Space to Unitary Group
- computation of homology group
- The Fundamental Group
- Generic Intersection of non-planar Surfaces in R^4
- Homology of CP^1, complex projective 1-space
- Symmetric Tensors and p-Forms
- Tiling the faces of a polygon/polytope
- About Singular Simplex
- Cofinite Topology
- Apparent Contradiction: Every Map from a Contractible Space to any X is trivi
- CP^2 , and CP^2 -bar, are not diffeomorphic.
- Fundamental Group
- Homeomorphism example
- What's the difference between differential topology and algebraic topology?
- Fundamental group with n holes
- real projective plane
- help me learn the GR cartan formalism
- Triangulation of Torus, Algorithms for Calculating Simplicial Homology
- Continuous bijection that is not an embedding
- Transfinite donuts?
- Quotient Spaces/Homeomorphic spaces?
- Topologize by convergence
- exact forms on the 2 torus
- Neumann boundary conditions on S^1/Z_2
- Postulates that Euclid neglected to mention?
- Haar-measure
- Euler Characteristic
- exterior derivative
- fundamental group to second homology group
- Global Section of Fiber Bundles with Contractible Fiber
- Parallel transport invariance
- Are functionals united with the vector space which they operate on?
- No difference between covectors and functions?
- Topology - help! Drowning student...
- Topology of Inhomogeneous 3-manifolds
- uniform continuity in top. spaces
- Tangent map, gauss map, and shape operator
- Request: Solved Problems in R.Geometry; Connections, etc.
- Cubes perspective
- What is the/a Quotient Bundle.?
- Lie algebra of the diffeomorphism group of a manifold.
- Laplacian of a 2-form
- Latitude-longitude coordinate range given radius
- bases in dual space
- naive question about differential forms
- homeomorphism
- problem with iterated integrals
- Boundary point
- Trivial Pi_1 and extending maps. Simple Question
- another proof that a vector field on the sphere must have a zero?
- Lie brackets and differential
- First Countable
- differentiable structures and diffeomorphisms
- How do I explain this?
- Technical Question, re: Le: Tensor of Cochain Complexes, and Isomorphism of Complexes
- k-connectedness and the homotopy-lifting property
- Latest research in fractal geometry
- How to prove these with Integral Theorems
- Hausdorff Space
- Five colors needed to cover two-sided plane?
- Conformally Flat and Einstein Geometry
- lie derivative versus covariant derivative
- open and closed
- A paradox about Maupertuis' principle (symplectic viewpoint)
- Coordinate independence of Lie derivative
- definition of *straight* lines...
- Area of circle using incribed polygons
- Closure of a one-parameter subgroup
- a line on a plane
- jacobian and diffeomorphism
- Differential geometry problem
- Area of standard-sized dartboard?
- Differential Geometry: Coordinate Patches
- 3 points on a line
- I have some trouble with the fourth spatial dimension
- Connected Sets
- Question about smoothness of a vector field (Reeb).
- Diagrammatic Tensor Notation from the Beginning
- Homeomorphism
- hyperbolic geometry
- reflection (matrices)
- Cross sectional area (NOT A QUESTION)
- Is "classical" differential geometry still useful?
- curvature tensor on product of riemanian manifold
- inverse function theorem for surface mappings
- homotopy
- Analytic Geometry - finding the normal vector at a point
- How do you get field solutions to Continuum Mechanics Problems?
- Hopf invariant
- p-norms for p<1
- What would this open set in R look like?
- Question about surfaces
- Game Theory - A graphical solution to all 2-person n x n strategy games?
- equivalent distances questions
- need help finding equation
- Circles
- Ricci form and Kahler manifolds
- Helix in cylindrical coords
- question about relationship between metrics
- Area of complex polygon?
- Geodesic Curvature of a curve on a flat surface
- A question on axiomatization of geometry
- why must a PB connection take values in Lie-algebra?
- Classifying Bundles; Fixed Base and Fiber
- derivatives in topology
- criteria for extension to cts fn between metric spaces?
- Tesseract with Time as Fourth Dimension
- why chern number must be an integer?
- toroidal helix in spherical coordinates?
- One form <-----> vector field
- Mathematical relationship to control camera heading
- bending of manifold and coordinate change
- Simple question on invariants and tensor rank
- why the basis of the tangent space of a manifold is some partials?
- Coordinate transformations question
- Local Maximum
- Lie algebraic decomposition
- Open sets and metric spaces...
- rotation matrix for azimuth and zenith angles
- the homotopy group of the projected space DP1
- Compact sets in Hausdorff space are closed
- lie derivative and vector field notion.
- Why isn't the volume of a pyramid Bh/2?
- Function Space C[a,b]
- Objective derivatives
- Topology of complex C^n space
- Vector projection in non-orthogonal coordinates
- Conformal invariance
- Curvature and Tangential angle
- Platonic Solids
- beautiful geometry proof
- 3d ellipse given two points
- Functional analysis
- Hausdorff condition in differential manifold definition
- one point set closed proof
- Confused about spinors a bit
- Would an energy diffraction ring in five space form a Minkowski space?
- Tautological line bundle?
- Smallest Set Containing All n-point Sets...
- Difference between SO(3) and so(3)
- 3rd grade geometry question
- Jacobian and the dimension of a variety
- 1D or 2D?
- Question about elementary topology
- infinite curve with two endpoints?
- What Does Mean Ortocrone Group
- "obvious" question on angles and solid-angles
- Drawing Braid diagrams in Latex
- Configuration centered at the origin
- Number of irreducible components of a variety
- Reeb graph
- Is pressure a rank 2 tensor?
- SO(3) as a quotient group of SU(2)?
- Closure and interior problem
- Calculating vanishing points with Linear Algebra.
- The volume of a spherical cap by integrating and using Cartesian coordinates
- ellipse from cone
- how to find a homotopy between two maps?
- Definition of neighborhood
- find the constant unknown angle of triangles series
- align 3d object to vector by rotation
- Square with edges, cube with faces identified.
- Example of a differentiable structure on R
- diam A = diam Cl(A) in metric space
- Volume between three surfaces
- Showing a graph is closed
- Hilbert's theorem and the pseudosphere
- euclidean geomtry question
- Countable base and subcover
- how to construct a map from S^2 to RP^2 with covering time being unity?
- Induced metric in submanifolds - What about the Christofells?
- Mappings on partitive sets
- General form of plane equation...
- DeRham Cohomology in Bott and Tu
- Extending Trivializations and Structure Groups
- Local Coordinates
- Differential forms as antiderivatives?
- projection of the co-derivative == co-derivative of the projection ?
- deg 1 map S^3 -> RP(3) ?
- Graphs, embeddings and dimensions
- how to judge whether a space has the fixed-point property?
- Determining Angle wrt to normal of a curved surface
- Problem With Explanation of Inner Product of Vector and Dyad
- Relationship betwen homotopy groups?
- Some Questions About Tensors
- Definition of Neighborhood, Very Confusing
- mod 2 products
- Basic geometry question regarding hexagons.
- Infine Direct Sum of Vector spaces
- how to understand that RP2 is non-orientable?
- Adjoint Representation of SO(3)
- Any closed interval [a,b] is compact ?
- Difference Between Vector and Tensor
- System above 3 coordinates
- inverse map of a one to one function
- Error in a book?
- Reflection across a Plane
- Generic coordinate systems
- Determining the line intersecting two planes
- Covariant and Contravariant Tensors
- Connected and compact space
- distance between point and curve
- Help With Raising and Lowering Indices
- spherical rolling
- Topological space satisfying 2nd axiom of countability
- Curves and parameters
- Spreading points evenly in plane
- Circular plane in a sphere
- Why does Chern class belong to INTEGER cohomology class?
- Dimensionality of Non-Euclidean geometry
- Going crazy trying to understand projective CP1 and CPn
- Please help me prove this:
- 3D Curvature
- Points on opposite sides a paper Mobius strip.
- Are these two shapes topologically same
- Question concerning compact subtopologies on Hausdorf spaces
- intersection producst on triangulated manifolds
- defition of lie derivatives
- Covariant and exterior derivatives
- Connections of degenerate metrics
- What's the fundamental group of a punctured torus?
- vertical and horizontal subspace of a vector space T_pP.
- Properties of Derivations and of Tangent Vectors
- "standard" Square is not a Smooth Submanifold of R^2
- Ellipse Major Axis Rotation
- Hyperbolic Distance Formula
- Tensor and geometric products
- a cohomology class on surfaces
- Euclidean space, euclidean topology and coordinate transformation
- Time Parameterizations and Diffeomorphisms
- discrete abelian subgroups
- Visualising sheaves and presheaves
- questions regarding tensors
- isotropy in torus-topology
- simplex splitting using center of gravity
- Tilt angle for a flat
- Projection of a differentiable manifold onto a plane
- Tangent to reparameterized curve
- No globally flat geometry on S²
- How to visualize CP^1 = S^2 ?
- Uniqueness of smooth structure
- DNA Topology
- Covariant derivative vs. Lie derivative
- Is a curved line 1 dimensional?
- Difference between covariant and contravariant levi-civita tensor?
- Eulerian Path problem
- A question about vector space manifold
- What shape would the arcade classic Asteroids' universe be?
- Solve cubic equations using neusis
- What would a 3D ball look like (in 3D) if it were partially in 4D space?
- Descent directions on manifolds
- parallel transport problem
- Boundaries and discrete spaces
- About coordinate transformations in general
- Geometry Question
- Is [a,b] ever an open set in the order topology?
- quotation about topolgy
- Cardinality/Function Question
- Topological spaces and basis
- Fitting Spheres into Arbitrary Geometry
- Cl(A) smallest closed set containing A.
- Is every manifold triangulable?
- metrizable space
- Rectangle question and closure of the interior?
- Can we homotope away a (non-trivial) knot.?
- why does removing a submanifold of codim 2 preserve connectivity?
- product of hausdorff spaces
- Volume of partial ellipsoid cut by plane
- a classical morse theory question
- Fitting a convex polytope into another convex polytope
- Metric Spaces and Compactness
- A circle where every chord intersects every other chord?
- Compactness and Metric Spaces
- Countable Complement Topology
- Fiber bundle basics
- An interesting problem (closure, limit points..)
- Frenet frame equations
- Image Topology detection
- Limit points and exterio points Quick quesiton
- A compact set question
- normal spherical image of x
- Dimension of a variety
- Largest rectangle in a cube
- Any good geometry resources?
- Simple Applications of Noncommutative Geometry?
- Question about Curvature
- Evenly spaced vectors in N-dim
- Compact Sets: Need help understanding...
- Morse function on a sphere
- Congruent Curves
- Differences between Algebraic Topology and Algebraic Geometry
- global diffeomorphism with tangent bundle
- Introduction to Dual Spaces
- product rule in Lie groups
- Probability measure on smooth functions
- defining a manifold without reference to the reals
- Bundle morphisms and automorphism
- Distance from centroid to surface of polyhedron as a function of frequency
- vertical and horizontal subspace
- bundle of 2 planes in R^4
- Calculate coordinate in 3D triangle.
- connection
- Topology and Convergence
- smooth manifold and constant map
- a piece of paper partially wrapped by a globe
- An inequality on the diagonals of a convex quadrilateral
- An inequality on the diagonals of a convex quadrilateral
- Product of pushforward
- Positioning B at the distance dz from A
- Hamiltonian flow
- Metric spaces RXR how to prove?
- Plotting a metric space a>0, c>0; 4ac-b2>0
- the endomorphisme bundle
- How to prove that a given set is a torus
- How this equation represent the equation of line?
- Seeking help with visualizing surface
- A path connected product of path connected spaces
- Octonians (new paper by Louis Kauffman and Jon Hackett)
- A question about continuity
- Euler class and Topological Invariants
- Gaussian Curvature of a cone...
- more than one right inverse
- Need help with metric space
- Intersection of complex sphere and cone
- smooth covering map and smooth embedding
- Nosecone Geometry
- Can a Center of a Sphere be conceived at infinity
- Problem in topology
- Proving a product of compact spaces is compact
- if a vector field has only nondegenerate zeros then the number of zeros is bounded
- cartan tensor
- Simple identity for antisymmetric tensor
- Paradromic Rings
- Non-linear forms & tensor densities
- Angles between 2 points along a varied path
- Spherical Trigonometry
- Calculating sphere orientation
- Special case of Stokes theorem
- Points for geometrical star
- Covariant Derivative
- 3D object inverted w.r.t. a sphere
- Pasch's Theorem for Asymptotic Triangles
- Trouble with Algebraic Geometry in General
- Curvilinear & Cartesian Conversions
- Compact Set in Metric Space
- Halves of two Opposite Arcs
- vectyor bundles with all zero characteristic classes
- Earth Map: Grid Projection
- metric
- Elementary geometry.
- Tychonoff's theorem and convergent subsequence
- Orientation preserving reparameterization
- "simple" 3d orbit question
- Example of Codimension-1 Manifolds that are not Isotopic.?
- Equivalence Bet. CW-complexes and Handlebodies.
- Angle of diagonal of a rectangular prism
- covariant derivative of the metric
- How does a matrix indicate a point?
- How to show 2-tori is diffeomorphic to S^3
- covariant derivate same as normal derivative?
- Calculating curvature indices
- Is every one-dimensional manifold orientable?
- Spherical law of cosines?
- operator
- Interpreting Intersection Form in H_1(K)
- Point set topology
- tangent bundle of vector space
- metric over submanifold
- Fibres of smooth manifolds
- Integration in Sean Carroll's "parallel propagator" derivation
- Eddington Finkelstein coordinates in the Schwarzschild spacetime
- Finsler geometry
- circle and square homeomorphism
- Surface parametrization
- exponential map of R3
- Fundamental group problem
- metric
- Converting Rotation Matrices (Left handed to Right handed)
- Zero curvature => straight line proof
- Symplectic form on a 2-sphere
- The Codimension of a singularity
- First fundamental form / eigenvalues
- metric spaces and infimums
- How to show that a transverse intersection is clean, but not conversely?
- Vector field as smooth embedding
- Nonvanishing section for direct sum of Mobius band
- stereographic projection
- Intersection Form Basics
- Mappings of Surfaces
- Calculate point off shortest distance between two skew lines
- Calculate point on line, perpendicular and intersecting another line in 3d space
- Differing definitions of an inner product
- Differential forms as sections
- Hausdorff dimension of the Cantor Set
- lie subgroup
- what is a twistor
- distances on flat manifolds
- universal cover
- covering action
- Covariant derivative and vector functions
- Minimal surfaces and asymptotic curves
- distances with non-euclidean metric
- 1-forme
- Converting longitude/latitude to x/y
- Problem in proving d(x,y)=0 implies x=y.
- Law of Cosines Homework problem
- Maurer-Cartan forms in physics
- Introduction to Topology Resources
- Homotopy and orientation preserving
- Spaces with constant curvature
- circle geometry
- tangent bundle
- Non degeneracy of critical points
- Gradient in terms of
- Covariance and contravariance
- differential geometry
- Geometric Example of Torsion Cycles and Relative Cycles (in Homology)
- Maximising the area of a triangle of known perimeter
- metric
- orientation form is closed
- maps from B2 to S2
- Cantor Set Characterization
- metric
- Hodge theory
- Differential Topology
- Converting Longitude and Latitude into Meters
- Find plane angle from pictures
- Complex-valued functions on a compact Hausdorff space.
- Periodic curve
- Is a bundle with non-orientable fibers always trivial?
- Distance formula in hyperbolic metric
- Mapping Class Group of Torus.
- Relative Boundary Operator
- Pyramidal frustums
- Ontoness and Induced Maps on Fundamental Group.
- computing fundamental group
- eulrt class of normal bundle
- Calculus of variations on odd dimensional manifolds
- Cometrics on Sub-Riemannian manifolds
- Why does a map from simply connected space to U(1) factors through R?
- Periodic curve as immersed submanifold
- Isotopy between overlapping and non-over. Dehn Twists.
- finding the slope??
- A question about the Urysohn metrization theorem
- "Handedness" of Mobius transformations
- Lebesgue measurable sets
- tangent bundle
- Equidistant curve of an ellipse
- fundamental group of matrices
- Combined Rotation
- covering spaces
- 2Questions: 1)Def. of Reg. Neighhoods 2)Zero in Homlgy and Hmtpy.
- Irreducible representations of SO(3)
- Question regarding Munkres' proof of the Tychonoff theorem
- Lattice growth formula
- Expressing cos(2π/n) without using trigonometric functions
- Manipulating vector-matrices combinations
- looking for an example
- mixed tensors in physics
- E+a lebesgue measurable
- A compactification theorem issue
- Nijenhuis bracket - am I crazy?
- Double application of Stokes' theorem to find the area of a simplex
- Help hermite curve vs sin
- vector-proof
- question about points on a circle ?
- question: vector integral in non-orthog coordinates
- Diffeomorphisms and embedded submanifolds
- Nature of SL(2,F5)
- Question about the Nagata-Smirnov metrization theorem
- Tychonoff theorem and Zorn's lemma
- The Bing metrization theorem
- homology cross product and orientation
- Curvature of level curve
- Mapping Class Group and Path-Component of Id.
- General Knots and Homology
- Some questions relating topology and manifolds
- Affine plane, block design
- Help on Jacobian Matrix for Cartesian to Spherical
- Sequences and nets
- Co-ordinate system
- fish cage geometry
- General Knots and Homology
- canonical orientation on level set submanifolds?
- Holonomy
- Tensor Rank of Stress Tensors
- Piecewise-linear ball complexes: calculations with GAP
- Planar/disc interaction
- interesting connections
- Solving for tent coordinates
- Locally Euclidean and Topological Manifolds
- Minimal compactification of an infinite dimensional space
- Every line bundle has a connection.
- Polygon detection
- Simple Question on Homotopy Equiv. and Contractible Subspaces
- triangle 2D projection to 3D
- Compact n-manifolds as Compactifications of R^n
- What does C^r-close mean?
- Finite intersection of closed sets is not necessarily closed
- how to show a mapping is a diffeomorphism
- Theory of calculating sphere centres from surface co-ordinates
- How accessible is Bott & Tu's book on algebraic topology?
- arbitrary product compactness
- Vectors in Cartesian Cylindrical Spherical
- Finite rank operators
- How do symplectic manifolds describe kinematics/dynamics ?
- Help for proving a mapping is a diffeomorphism
- Confusion on the definition of a quotient map
- Derive position on paper using sound waves?
- stereographic projection in R^4
- Parametrizations and regular curves
- Geometric construction of the square root
- geometric proof: minimum angle to point in a line segment
- Relationship between radius of curvature and slope
- Harmonic forms on resolved toric calabi yau spaces
- The lie brocket
- coordinate basis vs local frame?
- compact manifold
- Topology (specifically homotopy) question!
- geometry construction problem
- Closest approach of line segments
- normalized 2 dimensional parameter space
- lower limit topology
- Hausdorff measure calculation
- Graph of polar coordinate
- Descartes method for curvature
- Elliptic trigonometry
- Compact spaces
- Geodesic problem
- Set of Measure zero
- Homeomorphism classes of compact 3-manifolds
- Mapping preserving distance
- Show that there exists no sequence of functions satisfying the following
- convergence in the product and box topology
- Please help. Imposing a metric to preserve distance
- Homology of S3\knot
- elementary knot question
- Help with metric tensor in curvilinear coordinates on boundary
- Euclidean Killing Field Question
- Confused with closure and interior
- How to make a hodge dual with no metric, only volume form
- Topology questions (bases)
- Is Euclid's Postulate 5 really a "postulate of parallels"?
- Quick length of curve question
- an interesting math problem
- metrics question
- Product Topology and Compactness
- Topology and the Chinese Remainder Theorem?
- Alg. Topology! Help?
- Finding Convex Hulls in hyperbolic spaces
- Interesection Numbers in RP^3
- Riemannian manifold
- Length of a curve on a manifold
- Teaching myself Topology
- Caustic curves and dual curves
- Fractal Tiling of Rhombic Dodecahedra
- topology
- "Cauchy" Sequences in General Topological Spaces
- Periodic table of shapes to give a new dimension to maths
- Tensor Vs. Pseudotensor
- Question about a complex regarded as a topological space
- Finding a second point on a circle
- Layperson asking about circle sides (Warning! may not make sense)
- Interpretation of Curvature
- Differentiating a Linear Functional
- pathway to advanced geometry
- Kronecker Normal Form
- Intermediate Value theorem
- EM Differential Form version of Lagragian
- Flocking behavior
- Hypersurfaces of Euclidean space
- Existence of book on connection projective geometry and perspective?
- Quotient map theorem
- Simple question relating diffeomorphisms and homeomorphisms.
- Euclidean slices of constant r
- Theorem for fibration over R ?
- Manhattan on the line
- quasi-dimensional existance
- dual vector bundle E* is isomorphic to Hom(E, MXR)
- Topology problem...
- How to express a circle in spherical coordinates
- Naming a circle
- Mobius Geometry
- How do you construct the pattern of a dragonfly wing using the golden ratio?
- Equations for the Lawson Klein Figure
- Abelian Category
- Properties of Homeomorphisms between topological spaces
- Parallel transport on circle
- very basic question, open sets.
- eigenvalues of the Frenet formulas and angular velocity
- Munkres Acyclic Carrier
- Translations in polar coordinates
- Lie-algebraic elements as derivations.
- Principle fibre
- Ployhedron and Rectangle
- (anti)-symmetries of the Riemann curvature tensor
- Theorema Egregium
- Continuous functions that vanish at infinity
- Augmented reality rotation & zoom
- Natural Metrics on (Special) Unitary groups.
- Show: Every Fin.-Generated Group G is the Fund. Group of a 2-Complex (Reidemeister-Sc
- Total "absolute" curvature of a compact surface
- What does it mean by a Riemannian metric on a vector bundle?
- Invariant Polynomials on complexified bundles with connection
- tangent map
- locally compact
- connectedness
- Basic ellipse question
- Two definitions of locally compact.
- Which quantities are "naturally" forms, and which are (multi)vectors?
- Shared physical space
- Universal Euler class
- Griffiths Harris
- Gradient in Coordinates
- triangle and two circles theorem
- Differential of a Function
- Newton's Optimization Method
- Compact Sets of Moore Plane
- Topology proof
- Distance between a point on a sphere and a great circle arc
- Gauss Bonnet Theorem
- Surjection Between Mapping Class Grp. and Symplectic Matrices
- What is Euclid's Euclidean space?
- Place of Analytic geometry in modern undergraduate curriculum
- Finding the radius of three congruent tangential circles inside of a larger circle
- Discrete quotient group from closed subgroup
- Integration of differential forms
- Spivak's notation re. tangent buldles (Diff. Geom. Vol. 1)
- Irreducible components of affine Variety
- reasons for the identification of Ta(R^n) with Ta*(R^n)
- Topological and Metric Properties
- Calculate ellipse from 4 points?
- Existence of square circles
- Structuring the graph of |x| so it is not a smooth manifold
- conformal structures
- R^2 and R^2 - {(0,0)} are not homeomorphic
- Cartesian torque to Spherical Coordinates
- Relationship b/w Connectedness and Homeomorphisms
- Will limit of discrete steps give Pythagoras theorem?
- Why can finite elements handle complex geometries, but finite differences can't?
- Fitting an ellipse to a quadratic curve
- Towering strength
- Very simple question about homology
- PL: piecewise-linear topology and math physics with GAP
- coordinate tranformations on an embedded surface of in 3 space
- Do Homeomorphisms , Diffeomorphisms Preserve Intersections?
- Probability functions
- Special integration of Sphere Volume
- Definition of Normal (Intersection) Without Using a Metric
- Basis for First Homology: When can use Simple-closed Curves?
- How did trigonometry come about?
- Intersection Form With Coeffs. in Z/2
- orientability of sphere
- reduced homology of sphere cross reals?
- Change in Homology from Change in Coefficients
- why x,y,z?
- Tangent vectors as linear functionals on F(M)
- root grid
- Rainbow Spectrum Topology Map to Heightmap Grayscale.
- calculate reconstructionmatrix for ART
- four vertex theorem
- Why is this homology group is zero?
- Product of a finite complex and a point
- How to abelianizing the fundamental group?
- Relations between curvature and topology
- Complement of a Handlebody also a Handlebody?
- 2 dimensional quadratic forms
- morse theory
- Analitic Geometry
- what is affine hypersurface :(
- basis + covariant derivative question
- Manifold
- Finding default unit vectors in 3D modelling
- Topology + Probability
- Tensor products
- Does the presence of torsion require a non-symmetric metric?
- simply connected curve
- Constant curvature
- polar coordinate
- fuzzy manifold
- rolling: is the instantaneous axis of rotation tangential?
- Laplacian on Riemannian manifolds
- principal coordinates
- Volume of a Truncated Right Circular Cone
- Learning topology
- tangent+arctangent
- Odd notation for tensors
- Manipulation of tensor indices
- Problems like four-colour theorem
- curvature calculation
- Def. of (mod2) reduction of w in H_2(M,Z)
- Intersection Form of Connected Sum of CP^2
- basic tensor confusions
- orientation of 1-dim manifold
- compactness
- SIMPLE QUESTION! Open interval homeomorphic to R?
- Can I (& How to) figure out heading, bank, attitude of a flight w/this set of data ?
- vector geometry
- Topology of flat spatime -metric?
- Explanation of Hodge Decomposition
- Box counting dimension!! please help!!
- Fun Question: Embedding RP^3 into R^4
- Pi Paradox
- "Simple" geometry problem
- Tensor Analysis: quadric, bases, MOI, bisectors
- Fecko: Differential Geometry 2.3.1
- codifferential what is it ??
- Support Mapping of an Arbitrary Ellipsoid
- The 3D modeler, newbie and odd questions box!
- Fundamental Group of lens space
- Image Problem
- How many rectangles fit in a triangle?
- Rubik's Cube
- a Binary Operator Symbol Identification.
- Angle rotation about 2 axes
- Graph on the iPad
- Geometry Problem
- Lie Algebra of the reals with addition
- The meaning of "different" in Munkres' Topology
- Bachman on chains
- Problem with basic sets proof.
- Bachman's "line integral" versus "classical line integral"
- Can anyone give me the low down on Ceva's Theorem?
- Compact Spaces
- Paracompactness and metrizable manifolds
- Vector and Tensor problems
- Dense G-delta
- Vector Field
- Continuity, given topologies.
- Tractrix Reparametrization.
- homeomorphism
- 3-mfd
- Curl of Vector Fields
- Latus rectum for the non-mathematician
- intersection of hyperplane and n_cube having maximum number of non-adjacent vertices
- Do we know everything about 2d geometry?
- Radius of a circle that intersects two points on a right triangle.
- Contraction of the canonical symplectic form by vertical vectors
- Best Fit
- question about grad f on the x-y plane
- nonstandard terminology
- classifying manifolds
- Lie Groups
- Offset Circle Equation
- Volume of a prismatoid-ish
- Interpretiing the Dolbeault operators
- non-standard induced connection
- Principal Chiral Model
- find a constrained equilateral inner triangle of a triangle
- Symplectic geometry
- Orthonormal basis => vanishing Riemann curvature tensor
- how to measure perimeter without pi?
- Counter Intuitive result for Surface area of Helical Ribbon
- Basic Differential Forms Problem
- Convexity in the real projective plane?
- minimal surface ??
- How to show induced topological space
- Feasible to export and manipulate Mathematica animations in Powerpoint?
- retract and deformation retract >> plz
- n-torus question: tori tori tori
- First fundamental form and squared arc length element
- Topological Group Compact
- Planar Equations applied to Robotic Calibration
- codimension k stratum
- open sets in R being the union of open intervals
- Question about Stokes' Thm and Boundaries of Surfaces
- Looking for Gauss-Bonnet counterexample
- Affine geometry on PlanetMath
- (Hopefully)Very quick volume calculation question
- generalization of Theta operator to differential form
- Determine angle of intersecting lines inside a circle
- Homotopy extension property for CW pairs (Hatcher)
- delta vs simplicial complexes
- Finding radius given three points?
- Prove that diffeomorphisms are between manifolds with the same dimension
- Looking for a book
- Topolgy with Thoughtspacezero (youtube)(error?)
- is a (smooth) manifold allowed to have different dimensions in different points.
- Relations of an affine space with R^n , and the construction of Euclidean space
- Definite integral over SO(n)
- Geometry of physics
- Curve parametrization
- Another form of cubic folium equation
- Cup Product and Representability
- Expansion of the commutator of two vector fields
- How Does A Strain Tensor Transform?
- Action of Lie Brackets on vector fields multiplied by functions
- Complex Analysis/Topology Proof Help
- Covariant derivative vs Gauge Covariant derivative
- Part (a) of Theorem 2.27 in Rudin's POMA
- Books
- Determining the orientation of ellipsoids after 2 rotations
- Equation of Curve Using Arc Length and Two Points
- Manfold embeddings
- open set x open set
- Local Trivialization in Covering Spaces
- Symmetric Part of a Mixed (1,1) Tensor
- Homeomorphisms Send Bdries to Bdries
- 4D knots theory
- Proving that sup(X) exists for X nonempty and bounded
- Christoffel Symbols - Gauge Fields
- accumulation point of [0,1]
- Proving that if X is compact, X is closed
- calculating the killing vector fields for axial symmetry
- wedge product
- some questions about f*
- Metric Tensor for a Sphere
- convergence of a sequence of points on a manifold
- convention in parametric equation of parabola.
- manifold charts
- Diameter of Union of two sets
- Transformation to get a Lorentzian spherically symmetric metric to the Sylvester form
- topology question - need help
- topology question → What geometric figure?
- Transformation to get a metric to diagonal form
- What is a groupoid?
- Uncertain about premise for proof.
- Change in angle due to rotation
- definition of Lie derivatives
- what metric from given manifold?
- Basic thing of Conic in Projective Geometry
- Basic triangle plane geometry problem - impossible?
- Is the Transversal Intersection of Manifolds a Manifold?
- Dihedral angles for expanded icosidodecahedron.
- A compact, B closed Disjoint subsets of Metric Space then d(A,B)=0
- Product of Two Levi-Civita Symbols in N-dimensions
- Completeness of real numbers as Dedekind cuts
- why is homology isomorphic to reduced homology plus Z?
- Is every Closed set a complete space?
- Are 4-vectors vectors?
- Desargues Theorem Proof Using Homogeneous Coordinate
- Distance between point and 3D spline
- universal cover of figure-8
- Simplices and Triangulations
- Differential manifold without connection: Is it possible?
- Law of Sines (Elliptic, Hyperbolic, Euclidean)
- examples of infinite/arbitrary unions of closed sets that remain closed.
- Concerning charts on a manifold
- Question:calculation radius in steps of 3 degree
- Connected Sum of Orientable Manifolds is Orientable
- Conformal mapping of images
- Metric field and coordinate system
- Ellipses on spheres
- Characteristic Homology Classes
- Baby Do-Carmo's question.
- convergent subsequences in compact spaces
- Infinite intersection of indexed sets
- Infinite intersection of indexed sets
- Genus-g surface with Boundary and Dehn twists.
- Deriving Apoapsis and periapsis formulas
- Basic Confusion: Genus, Homology (Exm of Torus)
- Bounding Pairs of Dehn Twists are Trivial
- opposite of polygon?
- max/min packing density ratios
- fit a set of datapoints to another set
- product of compact sets compact in box topology?
- nonzero exact 1-form implies foliation?
- Open and closed sets in metric spaces
- Topological and neighbourhood bases
- some questions about maximum rank & typical rank
- Is this what you precisely do in co-ordinate transformations?
- special sequences in a product metric space
- metrics on the 2 sphere
- Homology and Integration; Req. for Proof.
- Which curved triangle is bigger?
- Isometry between euclidian and non-euclidian space
- Symplectic Basis on Sg and Non-Trivial Curves
- Time-dependent Riemannian metric
- Books on differential geometry on Banach Spaces.
- projective operator theory
- Sequences and closed sets.
- Cartesian product of separable metric spaces
- Proof of Jordan-Brouwer Separation Theorem Using Homotopy Theory?
- Dynamical systems notation
- two dissipation rate
- Topology Munkres answer
- Simple-Connectedness in Complex Plane: Def. in Terms of Riemann Sphere.
- playing with ms paint
- Variation of the metric tensor
- Quotients of Mapping Class Group Iso. to Symplectic Group.
- Complement of a 'Hood of the Solid Torus in S^4
- Difference between isomorphism and equality in graph theory?
- Tensor Multiplicatioin with Vectors
- Mapping Class Group of the Torus.
- Intersection and Coefficients
- Laplacian of the metric
- Distance between a point and a triangular plane segment
- Conic sections
- lemma 13.2 from Munkres
- Divergence of left invariant vector field
- what can rotation values imply on a sphere?
- Foliation of 4-dimensional connected Hausdorff orientable paracompact manifold
- Curves and torsion
- tangent vectors as equivalence classes of curves
- What is Unitary group U(2)
- Boundary and homeomorphism
- problems on smooth manifolds
- What are the open sets of U(N)?
- Did Curtis LeMay Discover Fractal Geometry in 1942?
- lie algebra
- Munkres text question.
- Normal form for Cubic
- Parametric helical surface
- Funny Universal Cover
- How important is topology for modern mathematics?
- Minimum height for fundamental domain of Gamma(2)
- Lie groups and non-vanishing vector fields
- Rotation matrix from vectors to cone
- Homology of Disjoint Union: Formalizing the Result.
- Def./Examples of Spin Structure Re Trivial Bundles?
- Using Jordan Curve Thm to Show H_n(R^n) Trivial?
- An detail in proving the homotopy invariance of homology
- How do you define the distance between two points in a non-flat 2-D space?
- Question about 30:60:90 (noob)
- de Rham's first theorem
- Generating Set for Mapping-Class Group of Genus-g Surface.
- Fine toplogy
- From plane to hyperplane in high dimension
- how far to moorseville?
- Limits first, then topology.
- invariants in fractal geometry
- Multiple views and projective geometry
- Polyline reshaping
- Null-homotopic, Retracts: Review for Prelims.
- Degree of a Map
- Introduction to Mainfolds Help
- Differentiable manifold
- Describing All covering Spaces of a Product Space
- Local Continuity and Restriction
- Induced Maps on Homology
- Mobius strip and spinors
- Symetry of an object
- Intro to Topology Recommended Texts
- Homemorphism between the set of circles with rational points and rectangles
- Continuous Bijection f:X-->X not a Homeo.
- Equation of a Plane in R^n , n>3
- Jordan-Brouwer Separation Theorem and Invariance of Domain
- Genus-g Surface and Retraction to Circle
- weird result on forms?
- Circular/Spiral Game Board Question
- Verifying the metric space e = d / (1 + d)
- highdimensional manifold reconstruction
- Ridge and valey lines mathematical definition?
- Can anyone check this identity please?
- 2 questions on coholomogy groups
- Is there a DeRham _Homology_?
- quick question - Christoffel Symbol Transformation Law
- Constructing Explicit Deformation Retractions
- Intersection of Planes in R^3 and Dense Subsets of R^3
- Covariant vector differentiation problem with kronecker delta?
- finding inverse of linear mapping
- Topology problems
- four color theorem problem
- Prime divisors hyperelliptic curves
- hyperbolic distance element
- Cantor Set/Space and Retracts.
- Generalizations (from metric to topological spaces)
- Geometric Interpretation of (lower) Cohomology?
- Principal divisor of a hyperelliptic curve
- Regular Surface definition
- Change of Coefficients in Homology and Individual Classes
- What is the value of perspective in number ?
- a straight line segment
- definition of a square
- How to prove alternating tensor(Levi-Civita symbol) is the only 3D isotropic tensor?
- Proper => Homeomorfismo
- Projections in Geometry (Question)
- Diffeomorphism of a disk and a square?
- finding hamilton path prove no hamilton circuit exists
- Lipschitz function and Baire Category Theorem
- Relation between a map and its lifting
- Making curves going through given points
- Angle on abstract metric space, has sense?
- graph coloring problem
- Dividing two differentials gives a total derivative... how?
- checking that a parametric curve is general helix
- 2D Circle and rectangle intersection tests
- Isometric Immersion of the Torus
- smooth manifolds and affine varieties
- Proposed: Quotient Space
- Geometrical Proofs
- I need help in this ques !!
- if every tangent line of a curve passes through a point, it is a line
- Transformation of angular and linear velocities
- Confusion on de Rham cohomology of manifolds
- Overhand knot efficiency
- f is diffeomorphism implys df is injective?
- 27 faceted cube: 2 omitted
- Torus: Mobius Strip Incisions
- The usual topology is the smallest topology containing the upper and lower topology
- Interesting shape on a cylinder
- On Alexandrov's theorem
- two manifold questions
- how to calculate the Poincare dual of a ray on R2-{0}?
- Calculating tangent spaces via curves.
- Tangent space basis
- [Topology] why the words "finer" and "coarser"?
- analytic and coanlytic sets
- Differentiating a function on a manifold
- Books for conic section
- Why the circle can't be homeomorphic to a real interval
- Analytic Geometry Question:
- Pull-back of vectors at a SINGLE point
- Can somebody give me both, an intuitive and a formal definition of a metric?
- John Lee,Smooth mfds exercise 2.16
- geodesic flows on compact surfaces
- Can the universe have a surface?
- Inside of a sphere
- Help with a metric tensor derivative
- Curvature form respect to principal connection
- curvilinear coordinate systems and "periodic" coordinates
- ALgebraic Topology Query (Hatcher) - Not Homework
- Lie derivative with respect to anything else
- How to find the class in H^*(M)?
- Simple Triangle/rectangle problem
- Conformal transformations and Möbius transformations
- Semidirect Product
- Geometry Proof (Circles and Chords)
- Complex Simplices
- Metric Space Explanation
- Is the cantor set diffeomorphic to the fat cantor set?
- optical conductivity & spectral weight
- Proof of V-E+F=2-2p (Euler's 2nd formula).
- Questions on connections and covariant differentiation
- Alg. Geom. Regular function confusion
- Question on 3 circles with changing values
- covariant derivative from connections
- Weird pattern within X-grams
- can these curves in the plane be geodesics?
- function whose cube is smooth
- Connecting homomorphism question
- bump functions
- On transition functions of fiber bundle
- Diameter into angles
- Good books for begining Lie algebra study
- Quick Question about Smooth Maps
- Confusion over the definition of Lie Derivative of a Vector Field
- Point-Set Question
- HW Question, either professor is wrong or I am.
- Riemannian surfaces as one dimensional complex manifolds
- Divergence of ( R + gR )
- Algebraic varieties in a minimal space
- Shutz's derivation of the Lie Derivative of a vector field
- Associating a Lie Algebra with a Lie Group
- topology munkres - urysohn lemma
- question on CP^n.
- How to define acos in relation to cos?
- Geometry: problem with defining the vertices of a tunnel around a given path
- Finding arbitrary circumference/circle on a sphere
- Sequence convergence proof
- How arbitrary are connections?
- calculating the gaussian curvature of a surface
- Ordering Line Segments to form a 2D Polygon after slicing a 3D Tri Map
- Empty Set Metric Space
- what flows on a surface can be geodesic flows?
- recomended differential topology books
- Finding interior angles of a quadrangle on sphere
- How to prove that SU(3) is compact
- Rotation around a tilted axis.
- Compactness of (0,1) when that is the whole metric space
- Given the 1st & 2nd fundamental forms, does a parametrization exist?
- Definition of tangent space on smooth manifolds
- An Engineer's Path to Topology
- Best Dover Math Books for Mathematician
- Must a contravariant contract with a covariant, & vice versa?
- Find Point on Rect Inside Circle Given Angle
- A question from Hatcher.
- Find Point On Rect Edge
- Extending a d-cohomology class to D-cocycle
- Sphere and hyperboloid intersection
- cone as surface....
- Pseudo-Riemannian tensor and Morse index
- How to geometrically think of a covector field..
- Torus and sphere with positive or negative curvature
- A simple Lie Group is linear
- If (X, d) and (X, r) are metric space, is {X, max(d, r)} necessary a metric space?
- Lie derivative of two left invariant vector fields
- lee 6.7
- is a tube always orientable?
- What is the Genus of Riemann Surface?
- möbius bundle
- why the Gaussian curvature is extrinsic ?
- Interior of Exterior of a looped domain
- Show that Area form is independent of parameterization?
- Manifold Question
- The Euler class of the unit tangent bundle to S^2
- identifying vertices of a planar diagram
- Is there a C^infty map that is one to one from R^n to R
- Is there any good reference on Riemann Surface and Riemann Theta Function?
- S^2 union a line connecting the north and south pole
- Geometry with Circle and Triangle
- Group of translations on real line with discrete topology
- Representation of algebra on a space of functions on real line with discrete topology
- Compactness is topology-independent ?
- distance between sets (a triangle-type inequality)
- Proof of expanding algebraic functions by Puiseux series
- what is a realization of this surface in Euclidean space?
- homeomorphism
- orientation sheaves
- Help with continuous functions in metric spaces
- Perturbation to free surface in bispherical coordinates
- Boundary points of subsets when viewed with the subset topology
- Circle Theorem Question
- Group Theory
- Problem with quaternion rotation maths
- A problem about equivalent metric
- Normed Linear Space - Query
- Something like a heliciod in S^3?
- Graphing a function in a Normed linear space
- A Question about Topological Connectivity
- Algebraic Curves
- Exterior derivative
- Covariant derivative of Lie-Bracket in normal orthonormal frame
- Help with reduction of En w/r/t linear manifold Em
- Projective half palne
- Interior Product
- Symplectic but Not Complex Manifolds.
- A question about subspace topolgy
- Ouroboros as a ball
- When can one reduce the structure group?
- Frustrated by this one exercise
- How to calculate the Euler class of a sphere bundle?
- Duality/Equivalence Between V.Fields and Forms (Sorry for Previous)
- Derivative of surface normal || tangent unit vector
- Sets intersection and the axiom of choice?
- curvilinear coordinates from orbits
- curl vs exterior derivative in spherical coords
- Christoffel Symbol blues
- What's necessary for transformations to be commutative?
- Locating the source of a sound
- Is the Levi-Civita connection unique for a given manifold?
- Parametric equation for 3D circle that's off-axis
- Oval VS Circle volume
- Fractal Behavior
- How can you drive the metric of kaluza klein in 5 D?
- Sphere/Atom packing - most efficient lattices?
- Cutting up squares
- Is this quantity a tensor and why?
- Determining Riemann surface geometry of algebraic functions
- Finding the a vector using angles
- Help me, nearest neighbor problem.
- [topology] new kind of separation axiom? where does it fit in?
- Curvature as the source of a field on a two dimensional Riemannian manifold
- Every uncountable subset of R has a limit point in Q?
- When to use alpha vs theta for angles
- Subscripted Index
- alternating and symmetric tensor
- Ricci tensor from Ricci 1-form
- Why "category" in Baire's Category Theorem?
- A Conceptual Question on de Rham cohomology.
- The length of a line intersecting a rectangle - not just diagonal!
- Solving for Christoffel Symbol
- dot product (scalar product) of 2 vectors: ABcos[itex]\theta[/itex]
- Help me find the shape
- Finding the (x, y, z) of a point on a sphere
- Counterexample "intersections of 2 compacts is compact"?
- Weak convergence of orthonormal sequences in Hilbert space
- Tasks of a regular tetrahedron
- How to find the radius of a circle by knowing two points and its arc length
- Domain of convergence of Puiseux series
- a problem on de rham cohomology
- Mobius strips and similar manifolds
- Example in topology: quotient maps and arcwise connected
- Homotopy paths
- Principal bundles with connections
- Non-embedded Manifolds: How do they happen
- metric function composed with concave function
- Looking for a metric to express difference between two curves
- Book on Curvature wrong or am I confused
- Rotational symmetry axis for 3D shape
- Gaussian curvature
- Very elementary differential geometry questions
- commutation property of covariant derivative
- compact manifold question
- Polygons can be designated as N-gons. What about vertices?
- Length of a line segment that binds the center of an ellipse with point of the elipse
- Quotientspace
- Empty set not in an ultrafilter
- 3D Vector resultant
- Fractal function
- How to View Tensors
- Product space
- Completeness of ℝ (when ℝ is defined abstractly)
- A metric space of equivalent sequence classes
- Cohomology with compact support
- Lie-Algebra of the SO(3,1)
- Isotropic surfaces questions...
- Algorithm for cutting a polygon into specific shapes
- Simple Geometry Question about a Complex Situation -Spherical/3D cartesian
- Closed Convex Cone
- back-projected ray in homogeneous coordinates
- Inverse images
- Is R mod 2pi a Compact Manifold?
- Geometric Proof of Ackerman (or Darwin, Jeantaud, Lankensperger) Steering: Explain?
- For what angles can the exact value of all trigonometrig ratios be found?
- Prove similarity (leading to a Pyth. proof)
- Ellipse inside a circle - intersection
- optimisation along a curve on a surface
- Is a convex subset of a connected space connected?
- Axial symmetry, non-rotating
- Center of an n-gon?
- pre-image open or not?
- Notation for set of limit points?
- Prop. 14 II Euclid Question
- SIN, COS, TAN help?
- Finding the Minor and major axis lenths of an ellipse from conjugate diameters
- Can a 4-D Hypercube be projected onto 3-space?
- Fiber Bundle Projection Map
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