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 Do non-orthogonal coordinate systems mean dependent coordinates?
  • gmmaro
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Graduate Nonautonomous Lie derivative
  • wrobel
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Graduate Equivalent definitions of tensor field
  • cianfa72
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Graduate Strain Tensor Based on Clifford Algebra
  • Arash1950
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Undergrad Differential Geometry with GNU/Linux
  • diegogarcia
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Undergrad About the maximal extension of local charts on a manifold
  • cianfa72
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Graduate On covariance of the Lagrange equations
  • wrobel
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Graduate Injective immersion and embedding
  • Korybut
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Undergrad Get geodesics & parallel transport on 2D surfaces (discrete timestep)
  • Tachytaenius
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Undergrad Compact manifold cannot be represented by (single) parametric equation
  • elias001
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Undergrad ##C^{\infty}##-module of smooth vector fields can lack a basis
  • cianfa72
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Undergrad Round 3-sphere symmetries as subspace of 4D Euclidean space
  • cianfa72
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Undergrad Differential structures over a topological manifold
  • cianfa72
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Undergrad ##SO(3)## topology
  • cianfa72
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Undergrad Pseudo-Riemaniann isometries
  • cianfa72
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Undergrad Spherically symmetric manifold
  • cianfa72
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Undergrad Smooth Manifold Chart Lemma
  • cianfa72
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Undergrad Vector fields wedge product vs covector field
  • cianfa72
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Undergrad Definition of a Manifold
  • littlemathquark
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Undergrad Chain Rule (partial derivatives): basic interpretation question
  • nomadreid
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Undergrad Definition of inertia tensor from a differential geometry viewpoint
  • cianfa72
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Undergrad Closed implies exact (differential 1-forms on R^2)
  • PhDeezNutz
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Undergrad Transformation of second rank tensor
  • LightPhoton
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Undergrad Differential structure on topological manifolds of dimension <= 3
  • cianfa72
  • · Replies 11 ·
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Undergrad Maximal atlas of topological manifold
  • cianfa72
  • · Replies 37 ·
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Undergrad Galilean spacetime as a fiber bundle
  • cianfa72
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Undergrad 2-sphere with any topology can't be homeomorphic to the plane
  • cianfa72
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Undergrad Must a Smooth Section Over a Mobius Strip Take Value Zero at Some Point?
  • cianfa72
  • · Replies 8 ·
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Undergrad Properties of the initial topology from a topological manifold
  • cianfa72
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Graduate Bachman : A geometric approach to differential forms
  • mrslamovics
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Undergrad Poincare lemma for one-form on ##\mathbb R^2 \backslash \{ 0 \}##
  • cianfa72
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High School Axes on a hyperbolic plane
  • BerryGo
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Undergrad On the definition of canonical coordinates in phase space
  • cianfa72
  • · Replies 9 ·
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Undergrad Confused about the inner product
  • Rick16
  • · Replies 58 ·
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Undergrad Induced metric in general case
  • gerald V
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Undergrad Dot product between basis vectors and dual basis vectors
  • Rick16
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Graduate Is the Lie derivative a tensor itself?
  • spinless
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Undergrad Is there a consensus about the meaning of the Christoffel symbols' indices?
  • Rick16
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Undergrad Help with area formula using direction cosines
  • davidwinth
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Undergrad Inner product of two tensors
  • Rick16
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Undergrad Question about Gradient's Domain and Range
  • littlemathquark
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Graduate Understanding: double of conformally flat manifold is conformally flat
  • kappaka
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Undergrad How to find inverse coordinates?
  • Rick16
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Undergrad The Road to Reality - exercise on scalar product
  • cianfa72
  • · Replies 36 ·
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Undergrad Trying to learn tensor algebra
  • Rick16
  • · Replies 8 ·
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Undergrad Notion of congruent curve along a vector field
  • cianfa72
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Undergrad Dirichlet problem boundary conditions
  • cianfa72
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Undergrad Which basis-forms are pseudo-tensors?
  • SiennaTheGr8
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Graduate Alternative topology of our 3D space
  • kochanskij
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Undergrad Manifold hypersurface foliation and Frobenius theorem
  • cianfa72
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Undergrad SL(n,R) Lie group as submanifold of GL(n,R)
  • cianfa72
  • · Replies 36 ·
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Undergrad Grassmannian as smooth manifold
  • Korybut
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Undergrad Can covariant derivative tensorialness be derived?
  • Pencilvester
  • · Replies 18 ·
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Undergrad Frobenius theorem applied to frame fields
  • cianfa72
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Undergrad 2-sphere manifold intrinsic definition
  • cianfa72
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Undergrad Radius of curvature formula when the denominator = 0
  • nomadreid
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Undergrad Quotient law and the curl in index notation
  • SiennaTheGr8
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Undergrad What is the difference between Gaussian and sectional curvature?
  • PhysicsRock
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Undergrad Do gradient and curl only differ by a Levi-Cavita tensor?
  • FQVBSina_Jesse
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High School Hopf fibration, Bloch sphere and quantum rotations - interactive site
  • vladramen
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Undergrad 3-parameter group of symmetries on the plane
  • cianfa72
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Undergrad Approximating smooth curved manifolds with "local bits" of curvature?
  • Spinnor
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Undergrad Conformal flatness of ellipsoid
  • ergospherical
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Undergrad Flat surface to curved surface
  • anilswipe
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Undergrad Definition of manifolds with boundary
  • PhysicsRock
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Undergrad When can I commute the 4-gradient and the "space-time" integral?
  • tannhaus
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Undergrad Spherical trig - sphere radius from 6 lengths
  • Vanadium 50
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Undergrad Identification tangent bundle over affine space with product bundle
  • cianfa72
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Undergrad Induced orientation on boundary of ##\mathbb{H}^n## in ##\mathbb{R}^n##
  • PhysicsRock
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Undergrad Resources on the Derivation of generalized Stokes' theorem
  • PhysicsRock
  • · Replies 11 ·
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Graduate How to switch from tensor products to wedge product
  • victorvmotti
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Undergrad A way to comprehend the geometry of a hypercube
  • Warp
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High School What would need to be possible to make a cube of circles?
  • SheldonCooper13
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Undergrad Degrees of Freedom in Lagrangian Mechanics for a Fractal Path
  • Pikkugnome
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Undergrad Is Diagrammatic Tensor Notation Widely Used in Mathematics?
  • Hill
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Graduate 3-connection on nontrivial topological 3-manifold
  • polology
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Undergrad Question regarding the 3-form ##dx^i \wedge dx^j \wedge dx^k##
  • PhysicsRock
  • · Replies 13 ·
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Undergrad Converse of focus-directrix property of conic sections
  • arham_jain_hsr
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Undergrad I need help generating a 2D representation of a curved plane
  • OlarFin
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Undergrad Short question about principal bundle
  • Korybut
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Undergrad Definition of tangent vector on smooth manifold
  • cianfa72
  • · Replies 21 ·
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Undergrad How to apply tensor transformation rule
  • guv
  • · Replies 9 ·
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Graduate What subset of a 3D space can be addressed by a single chart?
  • gnnmartin
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Undergrad Frobenius theorem for differential one forms
  • cianfa72
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Undergrad Dirac delta function in 2d polar coordinates
  • Trollfaz
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Graduate Differential structure of the group of automorphism of a Lie group
  • padawan
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Undergrad Invariance of a tensor of order 2
  • Thytanium
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Graduate What Is the Gauss Embedding Theorem Mentioned in the Video Talk?
  • The Tortoise-Man
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Undergrad Help with Differential Forms - self wedge product terms
  • thatboi
  • · Replies 13 ·
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Undergrad Rewriting Equation of Motion in terms of Dual Fields (Chern-Simons)
  • thatboi
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Undergrad Contact manifold and Darboux's theorem
  • cianfa72
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Undergrad Differential operator vs one-form (covector field)
  • cianfa72
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High School East-West error at regular points on the Azimuthal Equidistant Map
  • Miles Behind
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Undergrad How do I parametrize a conical/cylindrical surface in cylindrical unit vectors?
  • Trollfaz
  • · Replies 7 ·
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Undergrad How can a sphere be transformed using differential geometry?
  • James1355
  • · Replies 17 ·
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Undergrad Miller indices and periodic boundary conditions
  • Spathi
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Undergrad Trouble with metric. Holonomic basis and the normalised basis
  • GR191511
  • · Replies 6 ·
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Undergrad Also in 3D, two reflections make a rotation?
  • nomadreid
  • · Replies 2 ·
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High School How to find the infinitesimal coordinate transform along a hyperbola?
  • Sciencemaster
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Graduate Tensor/Vector decomposition/representation & DOF arguement
  • binbagsss
  • · Replies 2 ·
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