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.
A Variational derivative and Euler-Poincare equations
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A What is a differentiable variety?
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A How to calculate the matrix of a form?
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A Pathological example of a Principle Fiber Bundle?
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A Calculating Lie Derivative for Case (ii)
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I Component derivative of a tensor
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I Tangent spaces at different points
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I Tangent vector basis and basis of coordinate chart
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B Dimension of the metric of a projection of a sphere
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I Interpreting The Definition of Tensors
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I Tangent spaces at different points
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I Connections (principal bundles) ....
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I Understanding Differential Forms and Basis Vectors in Curved Space
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I Are Coordinates on a Manifold Really Functions from R^n to R?
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I Do index gymnastics change a tensor's dimensions?
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I Hopf fibration, stereoprojected fibers look close, can be?
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A Definition of Tensor and.... Cotensor?
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I What Does the $\star \sigma = 1$ Equation Reveal in Geometry?
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I Gradient vector without a metric
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A Lie derivative of vector field defined through integral curv
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A Invariance of Commutator Relations
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I How Are Basis Vectors Defined in Different Coordinate Systems?
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I Covariant Derivatives: Doubt on Jolt & Proving Zj Γjk Vi = 0
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I Christoffel symbol ("undotting")
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I Injective immersion that is not a smooth embedding
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I Differential structure on a half-cone
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A Intrinsic definition on a manifold
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A Fundamental definition of extrinsic curvature
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I Why vector lengths may not be preserved?
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B Differentiable function - definition on a manifold
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A Pullback of F on Manifolds: What Matrix Do We Take Determinant Of?
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I About the properties of the Divergence of a vector field
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A Is the Wedge Product of a 0-Form and l-Form Equal to f * η?
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A Differentiability of a function between manifolds
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A How Does the Chain Rule Define the Differential of a Function on a Manifold?
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I Why is the Alternator Alternating?
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I Rotating Coordinates: Solving for x and y
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I Differential of the coordinate functions
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A How do I pass a magnetic field to any coordinate system?
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A Coefficients in the linear combination of a k-form
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A Defining a Contact Structure Globally -- Obstructions?
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I Difference between vectors and one-forms
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A Hessian as "Square" of Jacobian?
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I Showing that the image of an arbitrary patch is an open set
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I Do Isometries Preserve Covariant Derivatives?
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I Differential for surface of revolution
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A The Distance between two points in a hypothetical universe
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I Connection forms and dual 1-forms for cylindrical coordinate
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I Christoffel symbol and Einstein summation convention
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I Riemann Tensor knowing Christoffel symbols (check my result)
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I How Is the Exponential Map Defined for Lie Groups Without a Metric?
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A Computing de Rham Cohomology of Connected Sums of Objects
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I Christoffel symbols knowing Line Element (check my result)
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A Penrose paragraph on Bundle Cross-section?
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I Problem: perturbation of Ricci tensor
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B Proving Linearity in Coordinate Transformation: A Mathematical Approach
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I What is the proof that the divergence is normal to the surface?
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I Lie derivative of a metric determinant
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I How to write the Frenet equations using the vector gradient?
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Possible Error in Vladimir Arnold Mathematical Methods C
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B How Many Parameters Are Needed to Parametrize the 3-Sphere?
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A Is Every Smoothly Extendable Submanifold Properly Embedded?
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A Finding the unit Normal to a surface using the metric tensor.
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A Constructing a sequence in a manifold
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I What is the Formula for Computing Surface Metric on a PF Surface?
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I Computation of the left invariant vector field for SO(3)
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I Meaning of cross terms in line element
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A Connection 1-forms to Christoffel symbols
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A Explicit examples of calculations of Chern classes
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A Family of curves tangent to a smooth distribution of lines
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A [Diff Forms & Skyrmions] What is this called?
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I Some Questions on Differential Forms and Their Meaningfulness
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A Coordinate representation of a diffeomorphism
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I Is the Proof of Statement (3) in Lipschultz's Differential Geometry Justifiable?
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I What is the covariant derivative of the position vector?
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I Metrics & Topologies: Do Different Metrics Induce Different Topologies?
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A Smoothness of multivariable function
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A Can Smooth Functions be Extended on Manifolds?
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I Is the Boundary Chart for a Closed Unit Ball Injective?
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A Question About Elementary Fiber Bundle Example
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I Does a covariant version of Euler-Lagrange exist?
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I Basic Q about Vector/tensor definition and velocity
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A What Is the Purpose of Exterior Forms in Differential Geometry?
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I Coherent operations on Jacobian matrices
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I Connections on principal bundles
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A Pushforward of Smooth Vector Fields
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I On the Gaussian Curvature of time-like surfaces
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I Understanding Fibre Bundles: A Layman's Guide
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A Characterizing the adjoint representation
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A How do dual vectors and tangent bases relate in coordinate functions?
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A Diagonalization of adjoint representation of a Lie Group
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I Deduce Geodesics equation from Euler equations
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I Coordinate systems vs. Euclidean space
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A Is tangent bundle TM the product manifold of M and T_pM?
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I Covariant derivative of Ricci scalar causing me grief
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I How is the Index Raised or Lowered on a Conformally Related Metric?
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I Why does a parallelizable manifold imply zero Riemann tensor?
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I Understanding Kunneth Formula and Tensor Product in r-Forms
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I How Does Nakahara Compactify I=[0,1] to S^1 in De Rham Cohomology Proof?
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I Understanding ##SO(2)## as Isotropy Group for ##x \in R^3##
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