Differential Geometry Forum

Post thread
Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
Undergrad What is Riemann's approach to classifying 2d surfaces?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Parallel Transport Along Geodesic
  • · Replies 6 ·
Replies
6
Views
4K
Graduate A claim about smooth maps between smooth manifolds
  • · Replies 20 ·
Replies
20
Views
5K
Graduate Calculate a tensor as the sum of gradients and compute a surface integral
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Hodge operator on 4th rank tensor
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How to prove that a scalar potential exists if the curl of the vector point function is zero?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad First algebraic Bianchi identity of Riemann tensor (cyclic relation)
  • · Replies 7 ·
Replies
7
Views
5K
Undergrad What is the Trace of a Fourth Rank Tensor in Index Notation?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Newmann-Penrose Spin coefficients for Schwarschild metric
  • · Replies 1 ·
Replies
1
Views
3K
Graduate In what representation do Dirac adjoint spinors lie?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Do diffeomorphisms have to be one-to-one functions?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate About lie algebras, vector fields and derivations
  • · Replies 20 ·
Replies
20
Views
4K
Graduate Hodge decomposition of a 1-form on a torus
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Is H a Lie Group with Subspace Topology from T^2?
  • · Replies 17 ·
Replies
17
Views
5K
Graduate About calculating a fundamental group
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Calculating the Hodge Star in the most general case
  • · Replies 29 ·
Replies
29
Views
4K
High School How to draw a plane intersecting a cylinder at a "compound angle"
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Infinitesimal Coordinate Transformation and Lie Derivative
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K
Graduate About computing the tangent space at 1 of certain lie groups
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Questions about algebraic curves and homogeneous polynomial equations
  • · Replies 4 ·
Replies
4
Views
3K
High School Attempted proof of the Contracted Bianchi Identity
  • · Replies 1 ·
Replies
1
Views
3K
High School Calculating the perfect tennis shot using vectors
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Metric of a Moving 3D Hypersurface along the 4th Dimension
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Reconciling 2 expressions for Riemann curvature tensor
  • · Replies 34 ·
2
Replies
34
Views
5K
Undergrad 4d integration/differentiation notation and the total derivative
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Integrability of the tautological 1-form
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Geodesic path in 2 dimensions?
  • · Replies 25 ·
Replies
25
Views
3K
Graduate Question of Cartan's structure equation (in Principal bundle)
  • · Replies 27 ·
Replies
27
Views
8K
Undergrad Triple equation for integral on a graph
  • · Replies 3 ·
Replies
3
Views
3K
Insights Yardsticks to Metric Tensor Fields
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad How can Euler angles be visualized using a polar plot?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the Coordinate-Free Formulation of the Hessian?
  • · Replies 8 ·
Replies
8
Views
5K
Graduate Problem in Understanding notation of distributional section
  • · Replies 1 ·
Replies
1
Views
2K
High School Geometric Issues with a line, a plane and a sphere...
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Is the projective space a smooth manifold?
  • · Replies 13 ·
Replies
13
Views
3K
High School Oriented Surfaces & Surface Area: Investigating the Impact
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Chiral symmetries in E[SUP]^n[/SUP]
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Are the coordinate axes a 1d- or 2d-differentiable manifold?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Prove $$T_{p}M$$ is a vector space with the axioms
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Assumptions about the convex hull of a closed path in a 4D space
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Triangles on Spheres: Isosceles and Shortest Distance Inferences
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Is my use of Einstein notation correct in this example?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What is the relationship between honeycombs and Minkowski space?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Dirac Notation for Vectors and Tensors (Neuenschwander's text ....)
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad The Inertia Tensor .... Determining Components of Angular Momentum ....
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Rich "isotropic tensor" concept
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What kind of tensor is the gradient of a vector Field?
  • · Replies 36 ·
2
Replies
36
Views
6K
Graduate Properties of adjacency matrix of graph with cycle
  • · Replies 3 ·
Replies
3
Views
11K
Undergrad Rotation of a vector along two axes (of which one is angle-dependent)
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad The best ways to display a map of non-Euclidean 3-D space?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Differential Forms or Tensors for Theoretical Physics Today
  • · Replies 70 ·
3
Replies
70
Views
16K
Graduate What Are the Key Concepts in Tensor Calculus?
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad A couple questions about the Riemann Tensor, definition and convention
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Christoffel Symbols: Difference, Importance & Uses
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Preservation of the angle between two vectors
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Is there research on 4D wave propagation in 3D solids?
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad How to visualize 2-form or exterior product?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Generic Curve in R^n: What We Know
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Transformation of connection coefficients
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Wedge product of a 2-form with a 1-form
  • · Replies 13 ·
Replies
13
Views
4K
High School What is the focus and parameter of a parabola with vertex off the origin?
  • · Replies 44 ·
2
Replies
44
Views
4K
Undergrad What is the construction of charts for the tangent bundle on the unit circle?
  • · Replies 8 ·
Replies
8
Views
3K
High School What is the Difference Between Circumscribed and Inscribed Squares?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Clarification about submanifold definition in ##\mathbb R^2##
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Maps with the same image are actually different curves?
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad Constructing an Oriented Atlas for S1 (Self Study)
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Proof of Frobenius' Theorem: Directly Showing ##\omega \wedge d\omega = 0##
  • · Replies 50 ·
2
Replies
50
Views
8K
Undergrad Diverging Gaussian curvature and (non) simply connected regions
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is differential about differential forms?
  • · Replies 21 ·
Replies
21
Views
4K
Undergrad Question regarding actual computation of tensor at point (Self Study)
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Roles of supersymmetry in mathematics?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Tangent Bundle of Product is diffeomorphic to Product of Tangent Bundles
  • · Replies 1 ·
Replies
1
Views
3K
High School Surface that when superimposed takes any one point to any other point
  • · Replies 29 ·
Replies
29
Views
2K
Undergrad Understanding Derivations and Tangent Spaces on Manifolds
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Geodesics with arbitrary parametrization
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding 3D circle parameterization
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Projection of 3D Plane from a certain perspective on the 2D Plane
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Jacobi identity of Lie algebra intuition
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Finding vertex of a 3D Triangle on a Plane
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Index Notation of div(a:b) and div(c^transpose d)
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What Is a Lie Group?
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Moving center of coordinates in the polar graph
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Excellent 3D Graphics thing at math3d.org
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Darboux theorem for symplectic manifold
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Differential k-form vs (0,k) tensor field
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Complete set of answers to Schaum's Tensor Calculus
  • · Replies 13 ·
Replies
13
Views
9K
Graduate Geodesics on three dimensional graph
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Array variable of envelope function (parameter representation)
  • · Replies 2 ·
Replies
2
Views
1K
MHB Taking Image of a curve about a given line
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Global coordinate chart on a 2-sphere
  • · Replies 37 ·
2
Replies
37
Views
6K
Undergrad What is this form of concavity called?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Fourier transform of a function in spherical coordinates
  • · Replies 10 ·
Replies
10
Views
6K
Undergrad What are the implications of Einstein's field equations having two free indices?
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Calculation for angular excess
  • · Replies 2 ·
Replies
2
Views
2K
High School Exploring Holonomic Basis in Cartesian Coordinates
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Morse Theory & Lagrangian Mechanics: Is There a Connection?
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Einstein summation convention confusion
  • · Replies 5 ·
Replies
5
Views
1K
High School Equation of Circle: Boundary or Surface?
  • · Replies 10 ·
Replies
10
Views
1K
High School Math Equation for Backward Going Curve?
  • · Replies 17 ·
Replies
17
Views
2K