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 Is H a Lie Group with Subspace Topology from T^2?
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A About calculating a fundamental group
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I Calculating the Hodge Star in the most general case
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A Infinitesimal Coordinate Transformation and Lie Derivative
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A About computing the tangent space at 1 of certain lie groups
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I Questions about algebraic curves and homogeneous polynomial equations
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B Attempted proof of the Contracted Bianchi Identity
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A Metric of a Moving 3D Hypersurface along the 4th Dimension
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I Reconciling 2 expressions for Riemann curvature tensor
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I 4d integration/differentiation notation and the total derivative
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I Integrability of the tautological 1-form
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A Question of Cartan's structure equation (in Principal bundle)
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I Triple equation for integral on a graph
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I What is the Coordinate-Free Formulation of the Hessian?
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A Problem in Understanding notation of distributional section
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I Is the projective space a smooth manifold?
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I Are the coordinate axes a 1d- or 2d-differentiable manifold?
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I Prove $$T_{p}M$$ is a vector space with the axioms
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I Assumptions about the convex hull of a closed path in a 4D space
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I Triangles on Spheres: Isosceles and Shortest Distance Inferences
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I What is the relationship between honeycombs and Minkowski space?
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I Dirac Notation for Vectors and Tensors (Neuenschwander's text ....)
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I The Inertia Tensor .... Determining Components of Angular Momentum ....
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I What kind of tensor is the gradient of a vector Field?
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Properties of adjacency matrix of graph with cycle
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I The best ways to display a map of non-Euclidean 3-D space?
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A Differential Forms or Tensors for Theoretical Physics Today
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A What Are the Key Concepts in Tensor Calculus?
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I A couple questions about the Riemann Tensor, definition and convention
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I Christoffel Symbols: Difference, Importance & Uses
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I Is there research on 4D wave propagation in 3D solids?
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I How to visualize 2-form or exterior product?
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I Generic Curve in R^n: What We Know
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I Transformation of connection coefficients
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I Wedge product of a 2-form with a 1-form
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I What is the construction of charts for the tangent bundle on the unit circle?
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B What is the Difference Between Circumscribed and Inscribed Squares?
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I Clarification about submanifold definition in ##\mathbb R^2##
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I Maps with the same image are actually different curves?
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I Constructing an Oriented Atlas for S1 (Self Study)
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Proof of Frobenius' Theorem: Directly Showing ##\omega \wedge d\omega = 0##
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I Diverging Gaussian curvature and (non) simply connected regions
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I What is differential about differential forms?
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I Question regarding actual computation of tensor at point (Self Study)
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A Roles of supersymmetry in mathematics?
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I Tangent Bundle of Product is diffeomorphic to Product of Tangent Bundles
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I Understanding Derivations and Tangent Spaces on Manifolds
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I Geodesics with arbitrary parametrization
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A Projection of 3D Plane from a certain perspective on the 2D Plane
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I Jacobi identity of Lie algebra intuition
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A What Is a Lie Group?
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I Darboux theorem for symplectic manifold
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I Differential k-form vs (0,k) tensor field
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Complete set of answers to Schaum's Tensor Calculus
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A Geodesics on three dimensional graph
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I Global coordinate chart on a 2-sphere
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I Fourier transform of a function in spherical coordinates
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I What are the implications of Einstein's field equations having two free indices?
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B Exploring Holonomic Basis in Cartesian Coordinates
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I Morse Theory & Lagrangian Mechanics: Is There a Connection?
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A Hilbert spaces and kets "over" manifolds
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Help requested with translating math into code (Not homework)
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A Differential forms on R^n vs. on manifold
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I Understanding Geodesic Parametrization on a Sphere
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A On the relationship between Chern number and zeros of a section
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I Definition of tangent space: why germs?
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I Transition Functions and Lie Groups
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I Is There a Distinction Between Riemann Metrics in Physics?
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B Ways to abstract curves or surfaces
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A Lagrangian for straight line in XY-plane (dependent on time)
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A Why are sheafs defined using abelian groups?
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A Something about configuration manifolds in classical mechanics
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A Connection between Reciprocal Space and Cotangent Space
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A On the different ways of determining curvature on manifolds
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A Information Geometry: Is there any there there?
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I What are the restrictions when swapping between geometries in physics?
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I Pushforward/Pullback of Vector Field
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A Transformation of coordinate basis
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B Examples of manifolds not being groups
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A Natural parametrization of a curve
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What is the Concept of Spectral Geometry?
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I Integration of differential forms
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I Parallel transport on flat space
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I Testing my knowledge of differential forms
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I Can Topological Spaces Have Properties Similar to Manifolds?
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I Prove the following statement about n-Manifolds
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I What is the Minkowski metric tensor's trace?
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What is a Fibre Bundle? A 5 Minute Introduction
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MHB Discrete Geometry: Info, Knowledge & More
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I Covariant derivatives, connections, metrics, and Christoffel symbols
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I Derived metrics on surfaces of positive curvature
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I Difference between diffeomorphism and homeomorphism
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I Fixing orientation by fixing a frame in a tangent space
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I Riemannian Fisher-Rao metric and orthogonal parameter space
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I How is this a representation of a 3 dimensional torus?
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B Can coordinates be functions in geometry?
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B Can Curvature and Geodesics be Generalized in Higher Dimensions?
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I What is an (almost) complex manifold in simple words
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I Infinitesimal Movement Along 3-d Geodesics
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A Parallel transport on a symplectic space
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