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.
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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MHB Angle between line and the axis
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High School Why Does Vqp Need to be Tangential to Vq in Order for Q to Get Closest to P?
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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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MHB Cos^2(∠POA)+cos^2(∠POB)+cos^2(∠POC)+cos^2(∠POD) is independent of P.
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MHB Calculating Coordinates of Spherical Triangles
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Undergrad Demo of cosine direction with curvilinear coordinates
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Undergrad On the Gaussian Curvature of time-like surfaces
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MHB What is the Maximum Inclination of a 3D Plane and its Equation in the XY Plane?
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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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High School Any geometrical meaning of multiplication of quaternions?
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MHB Translation Surfaces: Geometric Definition & Billiard Systems
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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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MHB Formula for changing a plane intersection angle
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High School Ellipse tangent line using projections
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High School Prove that tangents to the focal cord of parabola....
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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 Surface area of inner and outer halves of torus
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Undergrad Understanding Kunneth Formula and Tensor Product in r-Forms
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Undergrad How Does Nakahara Compactify I=[0,1] to S^1 in De Rham Cohomology Proof?
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Undergrad Understanding ##SO(2)## as Isotropy Group for ##x \in R^3##
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Undergrad Understanding the Wedge Product on a 3-dim Manifold
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High School What is the definition of a straight line in mathematics?
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Graduate On the dependence of the curvature tensor on the metric
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Undergrad Maurer-Cartan Form: Is it a One Form?
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Graduate Can you give an example of a non-Levi Civita connection?
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Undergrad Arbitrariness of connection and arrow on sphere
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Graduate Can I change topology of the physical system smoothly?
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Graduate Integration along a loop in the base space of U(1) bundles
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Undergrad Differential geometry in physics
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Graduate Which Mathematicians are focused on Hodge Conjecture?
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Undergrad Understanding De Rham's Period and Stokes Theorem
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Graduate Product of 3rd rank tensor with squared vector
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High School Eliminating Variables in Trigonometric Equations for Research Purposes
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Graduate Can I find a smooth vector field on the patches of a torus?
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Undergrad Coordinate transformation - Rotation
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Undergrad Convert from rectangular to Spherical Coordinates
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Graduate Find a circle inside of and tangent to a larger circle
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Graduate What's the Proper Way to Push Forward a Vector Field in Differential Geometry?
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Undergrad Left translate back to I in SO(3)
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Undergrad Calculate object distance by using just the parallax angles
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Undergrad Is this 4-Vector cross product calculation correct?
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Graduate Proving the Differential Map (Pushforward) is Well-Defined
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Graduate Need (or not) for invoking axiom of choice in a certain case
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Graduate Covariant derivative only for tensor
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Undergrad Is the Lorentz group non-compact?
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Undergrad Understanding Integration on an Orientable Manifold
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Graduate Compact Lie Group: Proof of Discrete Center & Finite Size?
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Undergrad Interior Product: Definition & Understanding
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Undergrad How Can Wedge Products Be Used in Differential Geometry?
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Undergrad Why Is the Lie Bracket a Vector Field on a Manifold?
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Graduate Christoffel symbols expansion for second derivatives
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Undergrad 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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Graduate Split the differential and differential forms
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Undergrad Problems in Differential geometry
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Graduate Understanding Metric Tensor Calculations for Different Coordinate Systems
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MHB Finding missing point of a vector when it is perpendicular to a line
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Graduate Understanding the Dual Basis and Its Directions
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Undergrad Transformation of covariant vector components
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Undergrad Hyperbolic space simulation in VR
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Undergrad Extrinsic Curvature Formulas in General Relativity: Are They Equivalent?
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Undergrad Question about Haar measures on lie groups
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MHB Distance between point and line
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Graduate Examples of application of transversality of submanifolds
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Undergrad Finding Killing Vectors for $$ds^2 = dr^2 + r^2d\theta^2$$
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Undergrad Volumes of n-Spheres: Intuition & Calculations
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Graduate Intution behind the definition of extrinsic curvature
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Undergrad Why Does the Area Element Vanish at the Origin in Polar Coordinates?
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Graduate Why Does Frankel Prefer Components on the Right in The Geometry of Physics?
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Undergrad Coordinate Charts: Clarifying Misunderstanding
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Undergrad Clifford Algebra and its contributions to physics
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Graduate Streamlines from strain rate tensor
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Undergrad Coordinate system vs ordered basis
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Undergrad Is My Understanding of the Generalized Stokes' Theorem Correct?
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Undergrad Product rule for exterior covariant derivative
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Undergrad Understanding Parallel Transport
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Undergrad Metric tensor derived from a geodesic
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Graduate Is Your Graph Homeomorphic to a Sphere?
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High School Achieving Rotational Symmetry with Tetrahedral Universal Joints
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Graduate LeviCivita in Orthogonal Curvilinear Coordinate System: "Cross Product Matrix
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Graduate Curvature of Flat Lorentz manifolds
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Undergrad Whats the meaning of Parallel in Vectors
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Graduate About Chern number of U(1) principal bundle on a torus
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Graduate Stokes' Theorem and Curvature on a Torus
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Undergrad Metric tensor : raising/lowering indices
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