Differential Geometry Forum

Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.

Threads

Graduate Proving Hopf Invariant and Degree of g for f⋅g

  • eok20
  • · Replies 2 ·
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Undergrad Analytic Geometry - finding the normal vector at a point

  • cfphys
  • · Replies 3 ·
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3

Graduate Is classical differential geometry still useful?

  • petergreat
  • · Replies 1 ·
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1

Graduate Smoothness of the Reeb vector field of a contact form

  • quasar987
  • · Replies 11 ·
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11

Graduate Definition of a homeomorphism between topological spaces

  • RedX
  • · Replies 10 ·
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10

Graduate Intersection of Connected Sets: True or False?

  • beetle2
  • · Replies 7 ·
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7

Graduate I have some trouble with the fourth spatial dimension

  • TubbaBlubba
  • · Replies 2 ·
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2

Graduate Arc length parameter for u¹ curves and metric tensor g₁₁

  • SNOOTCHIEBOOCHEE
  • · Replies 1 ·
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1

High School Area of standard-sized dartboard?

  • moonman239
  • · Replies 5 ·
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5

Graduate Relationship between Diffeomorphism and Jacobian

  • RedX
  • · Replies 12 ·
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12

High School What Defines a Straight Line?

  • tauon
  • · Replies 7 ·
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7

Graduate Area of circle using incribed polygons

  • Jamin2112
  • · Replies 11 ·
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11

Graduate Laplacian of 2-Form in R^3: Reference & Calculation

  • haushofer
  • · Replies 4 ·
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4

Graduate Closure of a one-parameter subgroup

  • eok20
  • · Replies 1 ·
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1

Graduate Conformally Flat and Einstein Geometry

  • charlynd
  • · Replies 4 ·
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4

Graduate Equivalence Relations on [0,1]x[0,1] and Hausdorff Spaces

  • lttlbbygurl
  • · Replies 2 ·
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Graduate Lie derivative versus covariant derivative

  • RedX
  • · Replies 3 ·
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3
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2

Graduate Differentiable structures and diffeomorphisms

  • RedX
  • · Replies 5 ·
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5

Graduate K-connectedness and the homotopy-lifting property

  • Bacle
  • · Replies 1 ·
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1

Graduate How to prove these with Integral Theorems

  • Gameowner
  • · Replies 3 ·
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3

Graduate Leray-Hirsch isomorphism and tensor product of cochain complexes

  • Bacle
  • · Replies 18 ·
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18

Graduate Is the Continuum Hypothesis Valid if the Interval is Wrapped into a Semi-Circle?

  • TheAlkemist
  • · Replies 2 ·
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2

Graduate Definition of boundary point and equation

  • wayneckm
  • · Replies 9 ·
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9

Graduate Continuous bijection that is not an embedding

  • Bacle
  • · Replies 8 ·
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8

Graduate What is the exterior derivative and how do you compute it?

  • Terilien
  • · Replies 18 ·
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18

Graduate Why Does an Isometry Preserve Lie Brackets Between Vector Fields?

  • rafax
  • · Replies 1 ·
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1

Graduate Proving the Inverse Function Theorem: A Struggle

  • lttlbbygurl
  • · Replies 1 ·
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1

Graduate Why are the differentials dx^μ used as dual space bases?

  • nklohit
  • · Replies 8 ·
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8

Graduate Residue calculus and gauss bonnet surfaces

  • zwoodrow
  • · Replies 5 ·
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5

Graduate What Is a Quotient Bundle?

  • Bacle
  • · Replies 8 ·
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8

Graduate Why is the iterated integral of two 1-forms homotopy invariant?

  • lavinia
  • · Replies 1 ·
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1

Graduate Uniform continuity in top. spaces

  • Bleys
  • · Replies 5 ·
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5

Graduate Request: Solved Problems in R.Geometry; Connections, etc.

  • WWGD
  • · Replies 3 ·
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3

Graduate Lie algebra of the diffeomorphism group of a manifold.

  • eok20
  • · Replies 7 ·
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7

Graduate Compute Euler Characteristic from Z Homology Dimensions

  • lavinia
  • · Replies 4 ·
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4

Graduate Tangent map, gauss map, and shape operator

  • badgers14
  • · Replies 1 ·
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1

Undergrad Postulates that Euclid neglected to mention?

  • LeonhardEuler
  • · Replies 2 ·
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Graduate Are functionals united with the vector space which they operate on?

  • jaketodd
  • · Replies 9 ·
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9

Graduate Is Parallel Transport Invariance Maintained in General Relativity Calculations?

  • bueller11
  • · Replies 10 ·
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Graduate No difference between covectors and functions?

  • mordechai9
  • · Replies 4 ·
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4

Graduate Exterior Derivative: Proving d^2 = 0 and d(w1 wedge w2) Properties

  • jem05
  • · Replies 6 ·
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6

Graduate Global Section of Fiber Bundles with Contractible Fiber

  • MagmaMorphic
  • · Replies 2 ·
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2

Graduate Fundamental group to second homology group

  • lavinia
  • · Replies 2 ·
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2

Graduate Proof of Real Projective Plane Embedding in R4

  • rainwyz0706
  • · Replies 2 ·
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2

Graduate Why does convergence in probability generate a topology but a.s. convergence does not?

  • wayneckm
  • · Replies 5 ·
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5

Graduate Intro to elementary index notation

  • fantispug
  • · Replies 1 ·
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1

Graduate Neumann boundary conditions on S^1/Z_2

  • AntideSitter
  • · Replies 3 ·
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3

Graduate What is the concept of exact forms on a 2 torus and how can it be visualized?

  • lavinia
  • · Replies 2 ·
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2

Graduate Math of Transfinite Donuts in 3-D Space

  • HarryWertM
  • · Replies 4 ·
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4

Graduate What's the difference between differential topology and algebraic topology?

  • petergreat
  • · Replies 5 ·
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5

Graduate Quotient Spaces/Homeomorphic spaces?

  • sutupidmath
  • · Replies 1 ·
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1

Undergrad Graphing Surfaces with Non-Linear Equations: What Are My Options?

  • aarciga
  • · Replies 2 ·
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2

Graduate Understanding Exterior Products of Multiple Vectors

  • jostpuur
  • · Replies 18 ·
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18

Graduate Can a Symmetric Tensor on a Manifold of Signature -+++ be Written in p-forms?

  • Phrak
  • · Replies 8 ·
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8

Graduate Cartan formalism for Christoffel symbols and curvature

  • zwoodrow
  • · Replies 2 ·
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2

Graduate Learn Conical Coordinates with Mathworld

  • TheDestroyer
  • · Replies 3 ·
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3

Graduate Fundamental group with n holes

  • madness
  • · Replies 8 ·
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8

Graduate Proof of Homeomorphism: An Example

  • beetle2
  • · Replies 4 ·
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4

Graduate Why Use 'Singular' to Describe Singular Simplex?

  • navigator
  • · Replies 3 ·
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3

Graduate Fundamental Group of (X,p): D^2\{(x,0) : 0<=x<=1}

  • Mikemaths
  • · Replies 3 ·
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3

Graduate Why aren't all closed loops at a point in the same homotopy class?

  • Zetta
  • · Replies 19 ·
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19

Graduate Homotopy from a loop to a point in contractible domain

  • Bacle
  • · Replies 9 ·
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9

Graduate Finite Complement Topology: Why It's the Finest

  • beetle2
  • · Replies 4 ·
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4

Graduate What is the boundary of a surface?

  • quasar987
  • · Replies 15 ·
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15

Graduate What Does the Homology Group Tell Us About a Manifold?

  • Sumanta
  • · Replies 4 ·
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4

Graduate Generic Intersection of non-planar Surfaces in R^4

  • Bacle
  • · Replies 2 ·
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2

Graduate What is the role of the transpose matrix in tensor transformations?

  • peterjaybee
  • · Replies 8 ·
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8

Undergrad Why Use Open and Closed Sets in Mathematical Proofs?

  • wayneckm
  • · Replies 8 ·
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8

Graduate Homology of CP^1, complex projective 1-space

  • Bacle
  • · Replies 1 ·
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1

Graduate Relation between Frenet-Serret torsion and the torsion tensor?

  • lucyk
  • · Replies 2 ·
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2

Graduate Levi-civita connection assumptions

  • RedX
  • · Replies 1 ·
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1

Graduate Identifying tiles in hyperbolic space?

  • Coin
  • · Replies 3 ·
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3

Graduate For M a 4-mfld., every class in H_2(M;Z) can be represented by a Surface.

  • Bacle
  • · Replies 13 ·
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13

Undergrad Tangent and normal vectors at a point on a circle through three points

  • CosmicVoyager
  • · Replies 3 ·
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3

Graduate Shortest arc between two points in polar coordinates

  • mnb96
  • · Replies 5 ·
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5

Graduate Geometric description of (simplicial)homologous cycles

  • Bacle
  • · Replies 6 ·
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6

Graduate Orientability of Complex Manifolds.

  • Bacle
  • · Replies 6 ·
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6

Graduate What is the difference between a manifold and a metric space?

  • RedX
  • · Replies 24 ·
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24

Graduate An intuitive explanation to the Killing equation?

  • kvf
  • · Replies 2 ·
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2

Graduate Can a disconnected space be a disjoint union of two infinite sets?

  • Mikemaths
  • · Replies 5 ·
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5

Graduate Need assistance,can you imagine a continuously deformation between X and Y?

  • kakarotyjn
  • · Replies 1 ·
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1

Undergrad Hyperbolic Geometry: Euclidean v 4D in 3D Space

  • Praxisseiz
  • · Replies 2 ·
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2

Graduate How to make curved line into torus?

  • CosmicVoyager
  • · Replies 1 ·
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1

Graduate Represntative Surfaces/Curves in homology. Examples.?

  • Bacle
  • · Replies 7 ·
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7

Graduate Good resources for symplectic manifold theorems easier than Arnold

  • Nusc
  • · Replies 9 ·
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9

Graduate Why is a contractible space simply connected if path connectedness suffices?

  • madness
  • · Replies 11 ·
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11

Graduate Is the square root loop from S^1 to RP^1 really a homeomorphism?

  • madness
  • · Replies 5 ·
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5

Graduate Sphere as an embedded submanifold

  • jem05
  • · Replies 6 ·
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6

Undergrad Definition of a line between two points on a sphere

  • TravelGirl
  • · Replies 13 ·
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13

High School Definition of the Cross Product?

  • 2^Oscar
  • · Replies 11 ·
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11

Undergrad How Does Horizontal Deviation Affect Elliptical Projection of a Sphere?

  • Chandi
  • · Replies 1 ·
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1

Undergrad How Can You Calculate the Distance Between Two Pulley Centers Using Belt Length?

  • itchy8me
  • · Replies 18 ·
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18

Graduate Is it possible to prove that any metric topology is Hausdorff?

  • sutupidmath
  • · Replies 4 ·
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4

Graduate Proving curl(∇v)ᵀ = 0 using indicial notation

  • traianus
  • · Replies 15 ·
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15

Graduate Can you compute Lie derivatives of tensors as commutators?

  • linford86
  • · Replies 8 ·
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8

Graduate Contraction map of geometric mean

  • rubinj
  • · Replies 2 ·
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2

Graduate Number of independent subcubes of a hypercube

  • twoflower
  • · Replies 1 ·
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1

Graduate Translation in Spherical Coordinates

  • karanmohan
  • · Replies 1 ·
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1

Graduate Can a Metric be Defined to Make All Balls in R^2 Unbounded with Shrinking Radii?

  • jostpuur
  • · Replies 7 ·
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7