Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
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Undergrad What Is the Geometrical Interpretation of Bounded Curves?
- wrobel
- · Replies 4 ·
Undergrad Family of Circles through Two Points: Exists Any Circle Beyond?
- Devil Moo
- · Replies 21 ·
Undergrad (2,0) tensor is not a tensor product of two vectors?
- voila
- · Replies 9 ·
Graduate How Is the Taylor Expansion Applied to Metric Tensors?
- mertcan
- · Replies 6 ·
Undergrad Do derivative operators act on the manifold or in R^n?
- orion
- · Replies 38 ·
Undergrad Finding Perpendicular Spirals in a Family of Curves
- IWantToLearn
- · Replies 3 ·
Graduate Question about Killing vector fields
- lichen1983312
- · Replies 4 ·
Graduate A question about coordinate distance & geometrical distance
- Frank Castle
- · Replies 13 ·
High School Velocity transformation from spherical to cartesian coords
- Stollaxel Stoll
- · Replies 2 ·
Undergrad Understanding the Transition Functions for S^1 Using Atlas Charts
- orion
- · Replies 3 ·
Undergrad Do Carmo's book, chap2 Regular surfaces, definition 1.2 -- question
- Jianphys17
- · Replies 7 ·
Graduate Question about Holonomy of metric connecton
- lichen1983312
- · Replies 6 ·
Undergrad Can there be a bounded space w/o a boundary w/o embedding?
- Pjpic
- · Replies 3 ·
Undergrad What is the Meaning of δ in δΓ?
- AleksanderPhy
- · Replies 7 ·
Undergrad Taylor expansion and parallel transport
- mertcan
- · Replies 2 ·
Graduate Confusion regarding conformal transformations
- nigelscott
- · Replies 4 ·
Graduate Geometrical interpretation of Ricci and Riemann tensors?
- Victor Alencar
- · Replies 1 ·
Undergrad Generalisation of Pythagoras theorem
- mertcan
- · Replies 2 ·
Graduate Transformation properties of the Christoffel symbols
- Chopin
- · Replies 2 ·
Undergrad Why a bijective map may not preserve area?
- Happiness
- · Replies 11 ·
Undergrad Covariant and contravariat components
- mertcan
- · Replies 2 ·
Undergrad The "real" angle between two triangular surfaces
- mbouksim
- · Replies 10 ·
Graduate Manifolds: local & global coordinate charts
- Frank Castle
- · Replies 40 ·
Undergrad Covariant derivative of a contravariant vector
- BiGyElLoWhAt
- · Replies 35 ·
Graduate Difficulty in understanding contracted Bianchi identities
- lichen1983312
- · Replies 5 ·
High School How Does Separating the Foci Affect the Shape of a Spheroid?
- DaveC426913
- · Replies 8 ·
Undergrad Decomposing the arc length of a circular arc segment
- jumbo1985
- · Replies 2 ·
Graduate Variation of Metrics: Formula & Proof Explained
- mertcan
- · Replies 1 ·
Undergrad Show the envelope of circles around a circle is a cardioid
- Happiness
- · Replies 5 ·
Undergrad Question about chart parameterization
- orion
- · Replies 6 ·
Undergrad Adjoint of the derivative in Minkowsky space.
- carllacan
- · Replies 6 ·
Undergrad Bounding the volume distortion of a manifold
- eyenir
- · Replies 2 ·
Undergrad Great Circle Distance Derivation
- IWantToLearn
- · Replies 3 ·
Graduate Derive General Metric Wave Equation
- mertcan
- · Replies 11 ·
Undergrad Is the Tensor Product of Two Matrices Really This Simple?
- space-time
- · Replies 1 ·
Undergrad What is the term for the velocity ##\boldsymbol v_e##?
- wrobel
- · Replies 13 ·
Graduate Expansion of covariant derivative
- mertcan
- · Replies 2 ·
Undergrad Curved space and curvilinear coordinates
- mertcan
- · Replies 6 ·
Graduate Riemann tensor and covariant derivative
- mertcan
- · Replies 5 ·
Undergrad Condition on vector field to be a diffeomorphism.
- kroni
- · Replies 3 ·
Graduate Non-Abelian Stokes theorem and variation of the EL action
- ShayanJ
- · Replies 4 ·
Graduate Möbius band diffrential geometry
- mertcan
- · Replies 16 ·
Undergrad Is that the definition of a lie group?
- davi2686
- · Replies 12 ·
Undergrad Observation of distances w.r.t. metric
- VladZH
- · Replies 16 ·
Graduate Normal velocity to the surface in Spherical Coordinate System
- Wisam
- · Replies 4 ·
Graduate Uniform grid of points on a sphere
- untarnished
- · Replies 12 ·
Graduate How can curl of 4-vector or 6-vector be writen?
- The Count
- · Replies 1 ·
Undergrad Defining a generalized coordinate system
- dipole
- · Replies 2 ·
Undergrad Triangles in different geometries
- GeometryIsHARD
- · Replies 1 ·
Graduate Continuous map from one manifold to another
- friend
- · Replies 1 ·
Graduate Integrating the topics of forms, manifolds, and algebra
- observer1
- · Replies 9 ·
Undergrad Study Reimann Geometry: High School+Astronomy
- jamalkoiyess
- · Replies 6 ·
Undergrad Derivation of equations using tensor
- TheCanadian
- · Replies 1 ·
Graduate Is the Inner Product in Quaternionic Vector Spaces Truly Hyperhermitian?
- Leditto
- · Replies 5 ·
Undergrad The geometry of manifolds .... (an essay by R.O.Wells Jr.)
- fresh_42
- · Replies 2 ·
Undergrad Spherical Geometry Equilateral Pentagon
- GeometryIsHARD
- · Replies 3 ·
Graduate Is the Dual Vector in Wald's Abstract Tensor Notation a Contraction?
- JonnyG
- · Replies 8 ·
Graduate Differentiation of a product of 4-gradients wrt a 4-gradient
- spaghetti3451
- · Replies 13 ·
Undergrad Riemann/Metric Tensor Calculator
- Isaac0427
- · Replies 2 ·
Undergrad Infinitesimal area element in polar coordinate
- arpon
- · Replies 4 ·
Undergrad 3D space curvature visualization
- VladZH
- · Replies 14 ·
Undergrad Difference between the projective space and one its part
- Ssnow
- · Replies 10 ·
Graduate Ellipse of transformation from spherical to cartesian
- octopode
- · Replies 8 ·
Graduate Field transformation under an active transformation
- spaghetti3451
- · Replies 1 ·
Undergrad What is the scale factor in orthogonal vector calculus?
- ElectricSenpai
- · Replies 1 ·
Undergrad What Is the Genus of One-Dimensional Curves?
- detre
- · Replies 1 ·
Undergrad Does an inverse Riemann exist?
- smilodont
- · Replies 9 ·
Undergrad Prove what the exterior derivative of a 3-form is....
- Fgard
- · Replies 4 ·
Undergrad Is a Riemannian Metric Invariant Under Any Coordinate Transformation?
- AlephClo
- · Replies 2 ·
Undergrad Velocity Vector Fields: Differentiating a Vector Function to Scalar
- dyn
- · Replies 8 ·
Undergrad Are the Two Equations for Push-Forwards in Differential Geometry Equivalent?
- dyn
- · Replies 7 ·
Graduate What math do I need to know to understand General Relativity
- Felix Quintana
- · Replies 36 ·
Undergrad Interior product with differential forms
- dyn
- · Replies 2 ·
Graduate Is the Riemann Curvature Tensor a Mathematical Tool or Physically Significant?
- superbat
- · Replies 4 ·
Undergrad Why are contravariant and covariant vectors important in general relativity?
- superbat
- · Replies 2 ·
Graduate Weyl Tensor Gravity propagation
- superbat
- · Replies 8 ·
Graduate Confusion on notion of connection & covariant derivative
- "Don't panic!"
- · Replies 42 ·
Graduate Mathematical Proof: Does Euclidian Geometry Hold in Riemannian?
- Patrick Sossoumihen
- · Replies 1 ·
Graduate Can geodesic deviation be zero while curvature tensor is not
- Elnur Hajiyev
- · Replies 2 ·
Graduate Project img on X-Y surface to a cylinder placed in center....
- Amirps
- · Replies 4 ·
Undergrad Directional Derivatives and Derivations - Tangent Spaces
- Math Amateur
- · Replies 4 ·
Undergrad Shape defined by x∈ℂ^3 and x⋅x = 0.
- Spinnor
- · Replies 6 ·
Finding the Rotation Vector $\omega$ of a Sphere
- evinda
- · Replies 1 ·
Graduate Derivative of smooth paths in Lie groups
- mnb96
- · Replies 10 ·
Undergrad Coordinates of Pushforwards .... General Case
- Math Amateur
- · Replies 9 ·
Graduate Pushforwards in local coordinates
- Math Amateur
- · Replies 6 ·
Graduate Computations with Tangent Vectors and Pushforwards - Lee
- Math Amateur
- · Replies 4 ·
Graduate Further Questions on Computations in Coordinates - Lee, Ch 3
- Math Amateur
- · Replies 2 ·
Graduate Maxwell's Equations in N Dimensions
- Hornbein
- · Replies 10 ·
Graduate Example of transversal submanifolds?
- aboutammam
- · Replies 6 ·
Undergrad Prerequisites for non Euclidean geometry
- Jianphys17
- · Replies 7 ·
Graduate Definition of chart for Lie groups
- mnb96
- · Replies 14 ·
Graduate Manifolds - Charts on Real Projective Spaces
- Math Amateur
- · Replies 8 ·
Graduate Tensor product of two arbitrary vectors an arbitrary tensor?
- sythrox
- · Replies 10 ·
Graduate Tangent Spaces of Parametrized Sets - McInerney, Defn 3.3.5
- Math Amateur
- · Replies 1 ·
Graduate Geometric Sets and Tangent Subspaces - McInnerney, Example 3
- Math Amateur
- · Replies 4 ·
Graduate Finding a New GPS Coordinate Between Two Lines on a Sphere
- frostfat
- · Replies 3 ·
Graduate Visualizing the space and structure described by a metric
- Whitehole
- · Replies 6 ·
Graduate Is Vector Integration Possible on Open N-1 D Surfaces in ND?
- Hornbein
- · Replies 9 ·
Graduate Understanding Covariant Derivative & Parallel Transport
- fab13
- · Replies 8 ·