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 Difference (if any) between E^1 x E^3 and E^4
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A Lie Algebra and Lie Group
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I Variation of geometrical quantities under infinitesimal deformation
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I Diffeomorphism invariance and contracted Bianchi identity
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I Bases for Tangent Spaces and Subspaces - McInerney Theorem 3.3.14
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I Algorithm to determine the roulette curve
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Minimal Surfaces, Differential Geometry, and Partial Differential Equations
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I Parameterized surfaces from coordinates
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A Tensor product of gradients
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A Transversality unlocks the secrets of the manifold?
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I Proving that an action is transitive in the orbits
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A Fractional spacetime, dimension equation
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I Derivative of a Tensor
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A Equivalence of diffeomorphism definitions
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A Logical foundations of smooth manifolds
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B Definition of coordinate system
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I Coordinate systems on the 2-sphere
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A Second order partial derivatives vanish?
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A Question about covariant derivatives
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I Set of possible rotations of a 3D object and the rotation history
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I Fourier transform on manifolds
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A Variational derivative of mean curvature
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I Deriving the spherical volume element
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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 Visualize the Hamiltonian
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A Pathological example of a Principle Fiber Bundle?
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I Deriving reduction formula in Geometric Algebra
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A Graphing Lie Derivative
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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 Differential forms and bases
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I Cordinates on a manifold
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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 Exploring Geometry: The $\star \sigma = 1$ Equation
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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?
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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 on a manifold
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I About the properties of the Divergence of a vector field
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A Exploring Wedge Product of 0-Form and l-Form
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A Differentiability of a function between manifolds
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A Differential of a function
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I Explanation of the Alternator
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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 Exponential map for Lie groups
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A Calculus of cohomology
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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 Coordinate Transformation
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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 Parametrization of the 3-sphere
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A First Variation of Jacobi Operator
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A Properly embedded submanifold
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A Normal to coordinate curve
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A Constructing a sequence in a manifold
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I Surface Metric Computation
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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 Unproven statement in a book
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Differential Geometry

Welcome to the Differential Geometry forum!

Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also.

Properties and fundamental geometric invariants of curves and surfaces in space; applications to the physical sciences. Pre: Calculus IV, and Introduction to Linear Algebra; or consent.

Differential and algebraic topology discussion. Homework help is available in the homework forums.

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