Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
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Graduate Why does velocity potential reduce degrees of freedom from 3 to 1?
- binbagsss
- · Replies 2 ·
Undergrad What does a complex vector "look" like?
- bsaucer
- · Replies 13 ·
Graduate Problems with the interpretation of the Torsion tensor and the Lie Bracket
- PhysicsObsessed
- · Replies 16 ·
Undergrad What is Riemann's approach to classifying 2d surfaces?
- AndreasC
- · Replies 6 ·
Undergrad Parallel Transport Along Geodesic
- diegogarcia
- · Replies 6 ·
Graduate A claim about smooth maps between smooth manifolds
- aalma
- · Replies 20 ·
Graduate Calculate a tensor as the sum of gradients and compute a surface integral
- Salmone
- · Replies 3 ·
Graduate Hodge operator on 4th rank tensor
- binbagsss
- · Replies 3 ·
Undergrad How to prove that a scalar potential exists if the curl of the vector point function is zero?
- immortalsameer13
- · Replies 2 ·
Undergrad First algebraic Bianchi identity of Riemann tensor (cyclic relation)
- binbagsss
- · Replies 7 ·
Undergrad What is the Trace of a Fourth Rank Tensor in Index Notation?
- binbagsss
- · Replies 4 ·
Graduate Newmann-Penrose Spin coefficients for Schwarschild metric
- vinicius_linhares
- · Replies 1 ·
Graduate In what representation do Dirac adjoint spinors lie?
- qft-El
- · Replies 1 ·
Undergrad Do diffeomorphisms have to be one-to-one functions?
- Antineutrino
- · Replies 1 ·
Graduate About lie algebras, vector fields and derivations
- aalma
- · Replies 20 ·
Graduate Hodge decomposition of a 1-form on a torus
- Mastermind01
- · Replies 2 ·
Undergrad Is H a Lie Group with Subspace Topology from T^2?
- yamata1
- · Replies 17 ·
Graduate About calculating a fundamental group
- aalma
- · Replies 2 ·
Undergrad Calculating the Hodge Star in the most general case
- Vanilla Gorilla
- · Replies 29 ·
High School How to draw a plane intersecting a cylinder at a "compound angle"
- bor
- · Replies 8 ·
Graduate Infinitesimal Coordinate Transformation and Lie Derivative
- Baela
- · Replies 1 ·
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
- iPuzzled
- · Replies 2 ·
Graduate About computing the tangent space at 1 of certain lie groups
- aalma
- · Replies 4 ·
Undergrad Questions about algebraic curves and homogeneous polynomial equations
- Bobby Lee
- · Replies 4 ·
High School Attempted proof of the Contracted Bianchi Identity
- Vanilla Gorilla
- · Replies 1 ·
High School 3D projectile motion vector for tennis with wind resistance
- themethetion
- · Replies 2 ·
Graduate Metric of a Moving 3D Hypersurface along the 4th Dimension
- victorvmotti
- · Replies 8 ·
Undergrad Reconciling 2 expressions for Riemann curvature tensor
- Shirish
- · Replies 34 ·
Undergrad 4d integration/differentiation notation and the total derivative
- binbagsss
- · Replies 1 ·
Undergrad Integrability of the tautological 1-form
- MathNeophyte
- · Replies 1 ·
Undergrad Geodesic path in 2 dimensions?
- James1238765
- · Replies 25 ·
Graduate Question of Cartan's structure equation (in Principal bundle)
- lichen1983312
- · Replies 27 ·
Undergrad Triple equation for integral on a graph
- NODARman
- · Replies 3 ·
Insights Yardsticks to Metric Tensor Fields
- fresh_42
- · Replies 7 ·
Undergrad How can Euler angles be visualized using a polar plot?
- DrDu
- · Replies 1 ·
Undergrad What is the Coordinate-Free Formulation of the Hessian?
- ergospherical
- · Replies 8 ·
Graduate Problem in Understanding notation of distributional section
- amilton
- · Replies 1 ·
High School Does a smaller sphere divide a larger sphere into two parts?
- dom_quixote
- · Replies 10 ·
Undergrad Is the projective space a smooth manifold?
- Delong66
- · Replies 13 ·
High School Does orientation affect the sign of a sphere's surface area?
- Trysse
- · Replies 5 ·
Undergrad Chiral symmetries in E[SUP]^n[/SUP]
- Mark Harder
- · Replies 1 ·
Undergrad Are the coordinate axes a 1d- or 2d-differentiable manifold?
- Delong66
- · Replies 4 ·
Undergrad Prove $$T_{p}M$$ is a vector space with the axioms
- Delong66
- · Replies 3 ·
Undergrad Assumptions about the convex hull of a closed path in a 4D space
- Arne
- · Replies 1 ·
Undergrad Triangles on Spheres: Isosceles and Shortest Distance Inferences
- Ahmed1029
- · Replies 8 ·
Undergrad Is my use of Einstein notation correct in this example?
- redtree
- · Replies 3 ·
Undergrad What is the relationship between honeycombs and Minkowski space?
- cuallito
- · Replies 1 ·
Undergrad Dirac notation for vectors in Neuenschwander section 1.9
- Math Amateur
- · Replies 16 ·
Undergrad Deriving the ith component of angular momentum from Neuenschwander equation 2.9
- Math Amateur
- · Replies 4 ·
Graduate Rich "isotropic tensor" concept
- apostolosdt
- · Replies 1 ·
Undergrad What kind of tensor is the gradient of a vector Field?
- GR191511
- · Replies 36 ·
Graduate Properties of adjacency matrix of graph with cycle
- asja
- · Replies 3 ·
Undergrad Rotation of a vector along two axes (of which one is angle-dependent)
- Andrea94
- · Replies 7 ·
Undergrad The best ways to display a map of non-Euclidean 3-D space?
- greswd
- · Replies 4 ·
Graduate Differential Forms or Tensors for Theoretical Physics Today
- kay bei
- · Replies 70 ·
Graduate Tensor operations, index notation, and applications in differential geometry
- trees and plants
- · Replies 9 ·
Undergrad A couple questions about the Riemann Tensor, definition and convention
- BiGyElLoWhAt
- · Replies 2 ·
Undergrad Christoffel Symbols: Difference, Importance & Uses
- dsaun777
- · Replies 7 ·
Graduate Preservation of the angle between two vectors
- LCSphysicist
- · Replies 9 ·
Undergrad Is there research on 4D wave propagation in 3D solids?
- ScientificMind
- · Replies 5 ·
Undergrad How to visualize 2-form or exterior product?
- lriuui0x0
- · Replies 5 ·
Undergrad Generic Curve in R^n: What We Know
- diffgeo4life
- · Replies 5 ·
Undergrad Transformation of connection coefficients
- accdd
- · Replies 7 ·
Undergrad Wedge product of a 2-form with a 1-form
- GR191511
- · Replies 13 ·
High School What is the focus and parameter of a parabola with vertex off the origin?
- rudransh verma
- · Replies 44 ·
Undergrad What is the construction of charts for the tangent bundle on the unit circle?
- Korybut
- · Replies 8 ·
High School What is the Difference Between Circumscribed and Inscribed Squares?
- A dummy progression
- · Replies 3 ·
Undergrad Is a smooth injective curve a diffeomorphism onto its image in ℝ²?
- cianfa72
- · Replies 4 ·
Undergrad Maps with the same image are actually different curves?
- cianfa72
- · Replies 21 ·
Undergrad Constructing an Oriented Atlas for S1 (Self Study)
- Amateur659
- · Replies 2 ·
Graduate Direct proof that ω∧dω=0 implies ω=αdβ
- WannabeNewton
- · Replies 50 ·
Undergrad Diverging Gaussian curvature and (non) simply connected regions
- Vini
- · Replies 1 ·
Undergrad What is differential about differential forms?
- pellman
- · Replies 21 ·
Undergrad Question regarding actual computation of tensor at point (Self Study)
- Amateur659
- · Replies 2 ·
Graduate Roles of supersymmetry in mathematics?
- arivero
- · Replies 6 ·
Undergrad Tangent Bundle of Product is diffeomorphic to Product of Tangent Bundles
- Amateur659
- · Replies 1 ·
High School Surface that when superimposed takes any one point to any other point
- simphys
- · Replies 29 ·
Undergrad Understanding Derivations and Tangent Spaces on Manifolds
- Korybut
- · Replies 7 ·
Undergrad Geodesics with arbitrary parametrization
- wrobel
- · Replies 3 ·
Undergrad Understanding 3D circle parameterization
- user1003
- · Replies 6 ·
Graduate Projection of 3D Plane from a certain perspective on the 2D Plane
- jisbon
- · Replies 2 ·
Undergrad Jacobi identity of Lie algebra intuition
- lriuui0x0
- · Replies 5 ·
Undergrad Finding vertex of a 3D Triangle on a Plane
- Anand Sivaram
- · Replies 3 ·
Graduate Index Notation of div(a:b) and div(c^transpose d)
- chowdhury
- · Replies 4 ·
Graduate What Is a Lie Group?
- joneall
- · Replies 11 ·
Undergrad Moving center of coordinates in the polar graph
- ektov_konstantin
- · Replies 2 ·
Undergrad Excellent 3D Graphics thing at math3d.org
- George Keeling
- · Replies 7 ·
Undergrad Darboux theorem for symplectic manifold
- cianfa72
- · Replies 4 ·
Undergrad Differential k-form vs (0,k) tensor field
- cianfa72
- · Replies 7 ·
Graduate Complete set of answers to Schaum's Tensor Calculus
- JTMetz
- · Replies 13 ·
Graduate Geodesics on three dimensional graph
- kairama15
- · Replies 9 ·
Graduate Array variable of envelope function (parameter representation)
- mk3
- · Replies 2 ·
Taking Image of a curve about a given line
- DaalChawal
- · Replies 1 ·
Undergrad Global coordinate chart on a 2-sphere
- cianfa72
- · Replies 37 ·
Undergrad What is this form of concavity called?
- pitaly
- · Replies 1 ·
Undergrad Fourier transform of a function in spherical coordinates
- redtree
- · Replies 10 ·
Undergrad What are the implications of Einstein's field equations having two free indices?
- snoopies622
- · Replies 14 ·
Undergrad Calculation for angular excess
- Haorong Wu
- · Replies 2 ·
High School Are cartesian coordinates the only holonomic orthonormal basis?
- mairzydoats
- · Replies 2 ·
Undergrad Morse Theory & Lagrangian Mechanics: Is There a Connection?
- dx
- · Replies 0 ·