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.
Undergrad What does a complex vector "look" like?
  • bsaucer
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Graduate Problems with the interpretation of the Torsion tensor and the Lie Bracket
  • PhysicsObsessed
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Undergrad What is Riemann's approach to classifying 2d surfaces?
  • AndreasC
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Undergrad Parallel Transport Along Geodesic
  • diegogarcia
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Graduate A claim about smooth maps between smooth manifolds
  • aalma
  • · Replies 20 ·
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Graduate Calculate a tensor as the sum of gradients and compute a surface integral
  • Salmone
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Graduate Hodge operator on 4th rank tensor
  • binbagsss
  • · Replies 3 ·
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Undergrad How to prove that a scalar potential exists if the curl of the vector point function is zero?
  • immortalsameer13
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Undergrad First algebraic Bianchi identity of Riemann tensor (cyclic relation)
  • binbagsss
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Undergrad What is the Trace of a Fourth Rank Tensor in Index Notation?
  • binbagsss
  • · Replies 4 ·
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Graduate Newmann-Penrose Spin coefficients for Schwarschild metric
  • vinicius_linhares
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Graduate In what representation do Dirac adjoint spinors lie?
  • qft-El
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Undergrad Do diffeomorphisms have to be one-to-one functions?
  • Antineutrino
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Graduate About lie algebras, vector fields and derivations
  • aalma
  • · Replies 20 ·
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Graduate Hodge decomposition of a 1-form on a torus
  • Mastermind01
  • · Replies 2 ·
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Undergrad Is H a Lie Group with Subspace Topology from T^2?
  • yamata1
  • · Replies 17 ·
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Graduate About calculating a fundamental group
  • aalma
  • · Replies 2 ·
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2
Undergrad Calculating the Hodge Star in the most general case
  • Vanilla Gorilla
  • · Replies 29 ·
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29
High School How to draw a plane intersecting a cylinder at a "compound angle"
  • bor
  • · Replies 8 ·
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8
Graduate Infinitesimal Coordinate Transformation and Lie Derivative
  • Baela
  • · Replies 1 ·
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Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • iPuzzled
  • · Replies 2 ·
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Graduate About computing the tangent space at 1 of certain lie groups
  • aalma
  • · Replies 4 ·
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Undergrad Questions about algebraic curves and homogeneous polynomial equations
  • Bobby Lee
  • · Replies 4 ·
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High School Attempted proof of the Contracted Bianchi Identity
  • Vanilla Gorilla
  • · Replies 1 ·
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High School Calculating the perfect tennis shot using vectors
  • themethetion
  • · Replies 2 ·
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Graduate Metric of a Moving 3D Hypersurface along the 4th Dimension
  • victorvmotti
  • · Replies 8 ·
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Undergrad Reconciling 2 expressions for Riemann curvature tensor
  • Shirish
  • · Replies 34 ·
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Undergrad 4d integration/differentiation notation and the total derivative
  • binbagsss
  • · Replies 1 ·
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Undergrad Integrability of the tautological 1-form
  • MathNeophyte
  • · Replies 1 ·
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Undergrad Geodesic path in 2 dimensions?
  • James1238765
  • · Replies 25 ·
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Graduate Question of Cartan's structure equation (in Principal bundle)
  • lichen1983312
  • · Replies 27 ·
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Undergrad Triple equation for integral on a graph
  • NODARman
  • · Replies 3 ·
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Insights Yardsticks to Metric Tensor Fields
  • fresh_42
  • · Replies 7 ·
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7
Undergrad How can Euler angles be visualized using a polar plot?
  • DrDu
  • · Replies 1 ·
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Undergrad What is the Coordinate-Free Formulation of the Hessian?
  • ergospherical
  • · Replies 8 ·
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Graduate Problem in Understanding notation of distributional section
  • amilton
  • · Replies 1 ·
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High School Geometric Issues with a line, a plane and a sphere...
  • dom_quixote
  • · Replies 10 ·
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Undergrad Is the projective space a smooth manifold?
  • Delong66
  • · Replies 13 ·
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High School Oriented Surfaces & Surface Area: Investigating the Impact
  • Trysse
  • · Replies 5 ·
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Undergrad Chiral symmetries in E[SUP]^n[/SUP]
  • Mark Harder
  • · Replies 1 ·
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Undergrad Are the coordinate axes a 1d- or 2d-differentiable manifold?
  • Delong66
  • · Replies 4 ·
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Undergrad Prove $$T_{p}M$$ is a vector space with the axioms
  • Delong66
  • · Replies 3 ·
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Undergrad Assumptions about the convex hull of a closed path in a 4D space
  • Arne
  • · Replies 1 ·
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Undergrad Triangles on Spheres: Isosceles and Shortest Distance Inferences
  • Ahmed1029
  • · Replies 8 ·
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Undergrad Is my use of Einstein notation correct in this example?
  • redtree
  • · Replies 3 ·
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Undergrad What is the relationship between honeycombs and Minkowski space?
  • cuallito
  • · Replies 1 ·
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Undergrad Dirac Notation for Vectors and Tensors (Neuenschwander's text ....)
  • Math Amateur
  • · Replies 16 ·
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Undergrad The Inertia Tensor .... Determining Components of Angular Momentum ....
  • Math Amateur
  • · Replies 4 ·
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Graduate Rich "isotropic tensor" concept
  • apostolosdt
  • · Replies 1 ·
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Undergrad What kind of tensor is the gradient of a vector Field?
  • GR191511
  • · Replies 36 ·
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Graduate Properties of adjacency matrix of graph with cycle
  • asja
  • · Replies 3 ·
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Undergrad Rotation of a vector along two axes (of which one is angle-dependent)
  • Andrea94
  • · Replies 7 ·
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Undergrad The best ways to display a map of non-Euclidean 3-D space?
  • greswd
  • · Replies 4 ·
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Graduate Differential Forms or Tensors for Theoretical Physics Today
  • kay bei
  • · Replies 70 ·
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Graduate What Are the Key Concepts in Tensor Calculus?
  • trees and plants
  • · Replies 9 ·
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Undergrad A couple questions about the Riemann Tensor, definition and convention
  • BiGyElLoWhAt
  • · Replies 2 ·
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Undergrad Christoffel Symbols: Difference, Importance & Uses
  • dsaun777
  • · Replies 7 ·
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Graduate Preservation of the angle between two vectors
  • LCSphysicist
  • · Replies 9 ·
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9
Undergrad Is there research on 4D wave propagation in 3D solids?
  • ScientificMind
  • · Replies 5 ·
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Undergrad How to visualize 2-form or exterior product?
  • lriuui0x0
  • · Replies 5 ·
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Undergrad Generic Curve in R^n: What We Know
  • diffgeo4life
  • · Replies 5 ·
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Undergrad Transformation of connection coefficients
  • accdd
  • · Replies 7 ·
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Undergrad Wedge product of a 2-form with a 1-form
  • GR191511
  • · Replies 13 ·
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High School What is the focus and parameter of a parabola with vertex off the origin?
  • rudransh verma
  • · Replies 44 ·
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Undergrad What is the construction of charts for the tangent bundle on the unit circle?
  • Korybut
  • · Replies 8 ·
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High School What is the Difference Between Circumscribed and Inscribed Squares?
  • A dummy progression
  • · Replies 3 ·
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Undergrad Clarification about submanifold definition in ##\mathbb R^2##
  • cianfa72
  • · Replies 4 ·
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Undergrad Maps with the same image are actually different curves?
  • cianfa72
  • · Replies 21 ·
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Undergrad Constructing an Oriented Atlas for S1 (Self Study)
  • Amateur659
  • · Replies 2 ·
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Graduate Proof of Frobenius' Theorem: Directly Showing ##\omega \wedge d\omega = 0##
  • WannabeNewton
  • · Replies 50 ·
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Undergrad Diverging Gaussian curvature and (non) simply connected regions
  • Vini
  • · Replies 1 ·
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Undergrad What is differential about differential forms?
  • pellman
  • · Replies 21 ·
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Undergrad Question regarding actual computation of tensor at point (Self Study)
  • Amateur659
  • · Replies 2 ·
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Graduate Roles of supersymmetry in mathematics?
  • arivero
  • · Replies 6 ·
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Undergrad Tangent Bundle of Product is diffeomorphic to Product of Tangent Bundles
  • Amateur659
  • · Replies 1 ·
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High School Surface that when superimposed takes any one point to any other point
  • simphys
  • · Replies 29 ·
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Undergrad Understanding Derivations and Tangent Spaces on Manifolds
  • Korybut
  • · Replies 7 ·
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Undergrad Geodesics with arbitrary parametrization
  • wrobel
  • · Replies 3 ·
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Undergrad Understanding 3D circle parameterization
  • user1003
  • · Replies 6 ·
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Graduate Projection of 3D Plane from a certain perspective on the 2D Plane
  • jisbon
  • · Replies 2 ·
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Undergrad Jacobi identity of Lie algebra intuition
  • lriuui0x0
  • · Replies 5 ·
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Undergrad Finding vertex of a 3D Triangle on a Plane
  • Anand Sivaram
  • · Replies 3 ·
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Graduate Index Notation of div(a:b) and div(c^transpose d)
  • chowdhury
  • · Replies 4 ·
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Graduate What Is a Lie Group?
  • joneall
  • · Replies 11 ·
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Undergrad Moving center of coordinates in the polar graph
  • ektov_konstantin
  • · Replies 2 ·
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Undergrad Excellent 3D Graphics thing at math3d.org
  • George Keeling
  • · Replies 7 ·
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Undergrad Darboux theorem for symplectic manifold
  • cianfa72
  • · Replies 4 ·
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Undergrad Differential k-form vs (0,k) tensor field
  • cianfa72
  • · Replies 7 ·
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Graduate Complete set of answers to Schaum's Tensor Calculus
  • JTMetz
  • · Replies 13 ·
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Graduate Geodesics on three dimensional graph
  • kairama15
  • · Replies 9 ·
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Graduate Array variable of envelope function (parameter representation)
  • mk3
  • · Replies 2 ·
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Taking Image of a curve about a given line
  • DaalChawal
  • · Replies 1 ·
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Undergrad Global coordinate chart on a 2-sphere
  • cianfa72
  • · Replies 37 ·
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Undergrad What is this form of concavity called?
  • pitaly
  • · Replies 1 ·
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Undergrad Fourier transform of a function in spherical coordinates
  • redtree
  • · Replies 10 ·
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Undergrad What are the implications of Einstein's field equations having two free indices?
  • snoopies622
  • · Replies 14 ·
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Undergrad Calculation for angular excess
  • Haorong Wu
  • · Replies 2 ·
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High School Exploring Holonomic Basis in Cartesian Coordinates
  • mairzydoats
  • · Replies 2 ·
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Undergrad Morse Theory & Lagrangian Mechanics: Is There a Connection?
  • dx
  • · Replies 0 ·
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Undergrad Einstein summation convention confusion
  • dyn
  • · Replies 5 ·
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