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.
Graduate Family of curves tangent to a smooth distribution of lines
  • · Replies 5 ·
Replies
5
Views
2K
Graduate [Diff Forms & Skyrmions] What is this called?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Coordinate representation of a diffeomorphism
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Smoothness of multivariable function
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Can Smooth Functions be Extended on Manifolds?
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Question About Elementary Fiber Bundle Example
  • · Replies 6 ·
Replies
6
Views
3K
Graduate What Is the Purpose of Exterior Forms in Differential Geometry?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Pushforward of Smooth Vector Fields
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Characterizing the adjoint representation
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How do dual vectors and tangent bases relate in coordinate functions?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Diagonalization of adjoint representation of a Lie Group
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Is tangent bundle TM the product manifold of M and T_pM?
  • · Replies 55 ·
2
Replies
55
Views
9K
Graduate On the dependence of the curvature tensor on the metric
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Can you give an example of a non-Levi Civita connection?
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Can I change topology of the physical system smoothly?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Integration along a loop in the base space of U(1) bundles
  • · Replies 12 ·
Replies
12
Views
3K
Graduate Which Mathematicians are focused on Hodge Conjecture?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Product of 3rd rank tensor with squared vector
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Can I find a smooth vector field on the patches of a torus?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Find a circle inside of and tangent to a larger circle
  • · Replies 23 ·
Replies
23
Views
4K
Graduate What's the Proper Way to Push Forward a Vector Field in Differential Geometry?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Proving the Differential Map (Pushforward) is Well-Defined
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Need (or not) for invoking axiom of choice in a certain case
  • · Replies 69 ·
3
Replies
69
Views
6K
Graduate Covariant derivative only for tensor
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Compact Lie Group: Proof of Discrete Center & Finite Size?
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Christoffel symbols expansion for second derivatives
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Split the differential and differential forms
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Understanding Metric Tensor Calculations for Different Coordinate Systems
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Understanding the Dual Basis and Its Directions
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Examples of application of transversality of submanifolds
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Intution behind the definition of extrinsic curvature
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Why Does Frankel Prefer Components on the Right in The Geometry of Physics?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Is Your Graph Homeomorphic to a Sphere?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate LeviCivita in Orthogonal Curvilinear Coordinate System: "Cross Product Matrix
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Curvature of Flat Lorentz manifolds
  • · Replies 31 ·
2
Replies
31
Views
6K
Graduate About Chern number of U(1) principal bundle on a torus
  • · Replies 28 ·
Replies
28
Views
7K
Graduate Stokes' Theorem and Curvature on a Torus
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Extracting Tensor Algebra Term with SU(N) Generators and Numbers
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is there a natural paring between homology and cohomology?
  • · Replies 19 ·
Replies
19
Views
4K
Graduate Can the Frenet Serret Frame Aid in Arc Length Parameterizations?
  • · Replies 19 ·
Replies
19
Views
4K
Graduate Is the Gradient a Covector and the Cross Product a Pseudovector?
  • · Replies 20 ·
Replies
20
Views
4K
Graduate Diffeomorphisms & the Lie derivative
  • · Replies 9 ·
Replies
9
Views
4K
Graduate About the nodal line in defining Euler angles
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Pullback and Pushforward in Manifolds: Why Do We Do It?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Conformal flatness of Riemannian manifolds
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Tangent Bundle: Why It's Important
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Methods to interpolate surfaces from gradient field?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Principal bundle triviality, groups and connections
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Very basic question about cohomology.
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Understanding Exact vs. Closed Forms for Mechanical Engineers
  • · Replies 3 ·
Replies
3
Views
4K
Graduate The meaning of an integral of a one-form
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Period matrix of the Jacobian variety of a curve
  • · Replies 2 ·
Replies
2
Views
2K
Graduate A question about split short exact sequence
  • · Replies 21 ·
Replies
21
Views
5K
Graduate What Determines the Degree of the Gauss Map in Differential Geometry?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Two cones connected at their vertices do not form a manifold
  • · Replies 14 ·
Replies
14
Views
6K
Graduate Metric on ℝ^2 Invariant under Matrix Transformations
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Oscillating Plane and Z axis - Energy Balance
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Difference between free G-action and effective G-action?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How Does the Volume Form on the Unit Sphere Relate to Its Position Vector?
  • · Replies 7 ·
Replies
7
Views
6K
Graduate Why the Chern numbers (integral of Chern class) are integers?
  • · Replies 12 ·
Replies
12
Views
7K
Graduate Theory of Surfaces and Theory of Curves Relationship
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Differential forms and vector calculus
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Interior products, exterior derivatives and one forms
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Torsion forms and particle physics
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Line integrals of differential forms
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Definition of the Lie derivative
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Square of the exterior derivative
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Ricci Form Notation: Need Help Understanding
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Action of a vector on the pull-back of a function
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Unique separation of the vertical and horizontal spaces?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Existence of Complex Structures and Characteristic Classes
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Maurer–Cartan forms for a matrix group?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Tangent Bundle questions about commutative diagram
  • · Replies 20 ·
Replies
20
Views
3K
Graduate How Is the Taylor Expansion Applied to Metric Tensors?
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Question about Killing vector fields
  • · Replies 4 ·
Replies
4
Views
2K
Graduate A question about coordinate distance & geometrical distance
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Question about Holonomy of metric connecton
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Confusion regarding conformal transformations
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Geometrical interpretation of Ricci and Riemann tensors?
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Transformation properties of the Christoffel symbols
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Manifolds: local & global coordinate charts
  • · Replies 40 ·
2
Replies
40
Views
8K
Graduate Difficulty in understanding contracted Bianchi identities
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Variation of Metrics: Formula & Proof Explained
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Derive General Metric Wave Equation
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Expansion of covariant derivative
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Riemann tensor and covariant derivative
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Non-Abelian Stokes theorem and variation of the EL action
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Möbius band diffrential geometry
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Normal velocity to the surface in Spherical Coordinate System
  • · Replies 4 ·
Replies
4
Views
3K
Graduate How can curl of 4-vector or 6-vector be writen?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Continuous map from one manifold to another
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Integrating the topics of forms, manifolds, and algebra
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Is the Inner Product in Quaternionic Vector Spaces Truly Hyperhermitian?
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Is the Dual Vector in Wald's Abstract Tensor Notation a Contraction?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Differentiation of a product of 4-gradients wrt a 4-gradient
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Ellipse of transformation from spherical to cartesian
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Field transformation under an active transformation
  • · Replies 1 ·
Replies
1
Views
1K
Graduate What math do I need to know to understand General Relativity
  • · Replies 36 ·
2
Replies
36
Views
6K
Graduate Is the Riemann Curvature Tensor a Mathematical Tool or Physically Significant?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Weyl Tensor Gravity propagation
  • · Replies 8 ·
Replies
8
Views
3K