Differential Geometry Forum

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Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
I Understanding the Wedge Product on a 3-dim Manifold
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B What is the definition of a straight line in mathematics?
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A On the dependence of the curvature tensor on the metric
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I Maurer-Cartan Form: Is it a One Form?
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A Can you give an example of a non-Levi Civita connection?
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I Arbitrariness of connection and arrow on sphere
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A Can I change topology of the physical system smoothly?
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A Integration along a loop in the base space of U(1) bundles
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I Differential geometry in physics
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I Understanding De Rham's Period and Stokes Theorem
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A Can I find a smooth vector field on the patches of a torus?
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A What's the Proper Way to Push Forward a Vector Field in Differential Geometry?
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I Left translate back to I in SO(3)
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I Calculate object distance by using just the parallax angles
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I Is this 4-Vector cross product calculation correct?
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A Proving the Differential Map (Pushforward) is Well-Defined
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A Need (or not) for invoking axiom of choice in a certain case
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A Covariant derivative only for tensor
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I Is the Lorentz group non-compact?
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I Understanding Integration on an Orientable Manifold
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A Compact Lie Group: Proof of Discrete Center & Finite Size?
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I Interior Product: Definition & Understanding
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I How Can Wedge Products Be Used in Differential Geometry?
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I Why Is the Lie Bracket a Vector Field on a Manifold?
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A Christoffel symbols expansion for second derivatives
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I What are the components of a vector field on a manifold?
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MHB The Fonz's Struggle with Geometry: Henry Winkler's Candid Confessions
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A Split the differential and differential forms
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I Problems in Differential geometry
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A Understanding Metric Tensor Calculations for Different Coordinate Systems
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A Understanding the Dual Basis and Its Directions
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I Transformation of covariant vector components
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I Hyperbolic space simulation in VR
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I Extrinsic Curvature Formulas in General Relativity: Are They Equivalent?
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I Question about Haar measures on lie groups
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A Examples of application of transversality of submanifolds
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I Finding Killing Vectors for $$ds^2 = dr^2 + r^2d\theta^2$$
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A Intution behind the definition of extrinsic curvature
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I Why Does the Area Element Vanish at the Origin in Polar Coordinates?
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A Why Does Frankel Prefer Components on the Right in The Geometry of Physics?
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I Coordinate Charts: Clarifying Misunderstanding
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I Clifford Algebra and its contributions to physics
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Streamlines from strain rate tensor
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I Coordinate system vs ordered basis
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I Is My Understanding of the Generalized Stokes' Theorem Correct?
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I Product rule for exterior covariant derivative
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I Understanding Parallel Transport
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I Metric tensor derived from a geodesic
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A LeviCivita in Orthogonal Curvilinear Coordinate System: "Cross Product Matrix
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A Curvature of Flat Lorentz manifolds
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I Whats the meaning of Parallel in Vectors
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A About Chern number of U(1) principal bundle on a torus
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A Stokes' Theorem and Curvature on a Torus
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I Metric tensor : raising/lowering indices
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I Levi-Civita properties in 4 dimensions
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I Understanding the Derivation of the Metric Tensor
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I Proving Stokes' Theorem: General Cases and the Fundamental Theorem of Calculus
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I Mean and Gaussian curvature for a Gaussian 'hill' seem wrong
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I Problem when solving example with differential forms
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I Integrals: Why Change from M to $\phi(M)$?
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A Extracting Tensor Algebra Term with SU(N) Generators and Numbers
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A Is there a natural paring between homology and cohomology?
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A Can the Frenet Serret Frame Aid in Arc Length Parameterizations?
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A Is the Gradient a Covector and the Cross Product a Pseudovector?
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I Worked example on a covariant vector transformation
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I Curvature forms and Riemannian curvatures of connections
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A Diffeomorphisms & the Lie derivative
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I Lie groups left invariant vector fields
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A Pullback and Pushforward in Manifolds: Why Do We Do It?
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I Chart coordinate maps of topological manifolds
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I Norm of Laplacian Let: Formula for | ∇X|² in Coordinates
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A Conformal flatness of Riemannian manifolds
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A Tangent Bundle: Why It's Important
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B What would things look like if PI = 3.
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A Methods to interpolate surfaces from gradient field?
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I Winding number for a point that lies over a closed curve
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A Principal bundle triviality, groups and connections
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I Ricci curvatures determine Riemann curvatures in 3-dimension
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I Difference between 1-form and gradient
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I Deriving Frenet-Serret Formulas: Why -τᴿ?
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I Is There a Faster Way to Prove Smoothness on Manifolds?
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I Conservation of dot product with parallel transport
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A Very basic question about cohomology.
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A Understanding Exact vs. Closed Forms for Mechanical Engineers
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A The meaning of an integral of a one-form
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A Period matrix of the Jacobian variety of a curve
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A A question about split short exact sequence
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A What Determines the Degree of the Gauss Map in Differential Geometry?
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A Two cones connected at their vertices do not form a manifold
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I Why Are Connection 1 Forms Essential in Principal G-Bundles?
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I How is a manifold locally Euclidean?
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A Metric on ℝ^2 Invariant under Matrix Transformations
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A Oscillating Plane and Z axis - Energy Balance
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A Difference between free G-action and effective G-action?
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I Computing the Weingarten Map L by raising an index
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A How Does the Volume Form on the Unit Sphere Relate to Its Position Vector?
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A Why the Chern numbers (integral of Chern class) are integers?
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I Commutator of covariant derivatives
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I Question About Curvilinear Cooridnates
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A Theory of Surfaces and Theory of Curves Relationship
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