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