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 On covariance of the Lagrange equations
- wrobel
- · Replies 1 ·
Undergrad Do non-orthogonal coordinate systems mean dependent coordinates?
- gmmaro
- · Replies 8 ·
Graduate Nonautonomous Lie derivative
- wrobel
- · Replies 0 ·
Graduate Equivalent definitions of tensor field
- cianfa72
- · Replies 5 ·
Graduate Strain Tensor Based on Clifford Algebra
- Arash1950
- · Replies 3 ·
Undergrad Differential Geometry with GNU/Linux
- diegogarcia
- · Replies 9 ·
Undergrad About the maximal extension of local charts on a manifold
- cianfa72
- · Replies 8 ·
Graduate Injective immersion and embedding
- Korybut
- · Replies 2 ·
Undergrad Get geodesics & parallel transport on 2D surfaces (discrete timestep)
- Tachytaenius
- · Replies 12 ·
Undergrad Compact manifold cannot be represented by (single) parametric equation
- elias001
- · Replies 5 ·
Undergrad ##C^{\infty}##-module of smooth vector fields can lack a basis
- cianfa72
- · Replies 9 ·
Undergrad Round 3-sphere symmetries as subspace of 4D Euclidean space
- cianfa72
- · Replies 6 ·
Undergrad Differential structures over a topological manifold
- cianfa72
- · Replies 4 ·
Undergrad ##SO(3)## topology
- cianfa72
- · Replies 29 ·
Undergrad Pseudo-Riemaniann isometries
- cianfa72
- · Replies 4 ·
Undergrad Spherically symmetric manifold
- cianfa72
- · Replies 10 ·
Undergrad Smooth Manifold Chart Lemma
- cianfa72
- · Replies 4 ·
Undergrad Vector fields wedge product vs covector field
- cianfa72
- · Replies 11 ·
Undergrad Definition of a Manifold
- littlemathquark
- · Replies 15 ·
Undergrad Chain Rule (partial derivatives): basic interpretation question
- nomadreid
- · Replies 5 ·
Undergrad Definition of inertia tensor from a differential geometry viewpoint
- cianfa72
- · Replies 15 ·
Undergrad Closed implies exact (differential 1-forms on R^2)
- PhDeezNutz
- · Replies 6 ·
Undergrad Transformation of second rank tensor
- LightPhoton
- · Replies 4 ·
Undergrad Differential structure on topological manifolds of dimension <= 3
- cianfa72
- · Replies 11 ·
Undergrad Maximal atlas of topological manifold
- cianfa72
- · Replies 37 ·
Undergrad Galilean spacetime as a fiber bundle
- cianfa72
- · Replies 16 ·
Undergrad 2-sphere with any topology can't be homeomorphic to the plane
- cianfa72
- · Replies 5 ·
Undergrad Must a Smooth Section Over a Mobius Strip Take Value Zero at Some Point?
- cianfa72
- · Replies 8 ·
Undergrad Properties of the initial topology from a topological manifold
- cianfa72
- · Replies 8 ·
Graduate Bachman : A geometric approach to differential forms
- mrslamovics
- · Replies 2 ·
Undergrad Poincare lemma for one-form on ##\mathbb R^2 \backslash \{ 0 \}##
- cianfa72
- · Replies 15 ·
High School Axes on a hyperbolic plane
- BerryGo
- · Replies 4 ·
Undergrad On the definition of canonical coordinates in phase space
- cianfa72
- · Replies 9 ·
Undergrad Confused about the inner product
- Rick16
- · Replies 58 ·
Undergrad Induced metric in general case
- gerald V
- · Replies 1 ·
Undergrad Dot product between basis vectors and dual basis vectors
- Rick16
- · Replies 17 ·
Graduate Is the Lie derivative a tensor itself?
- spinless
- · Replies 4 ·
Undergrad Is there a consensus about the meaning of the Christoffel symbols' indices?
- Rick16
- · Replies 2 ·
Undergrad Help with area formula using direction cosines
- davidwinth
- · Replies 3 ·
Undergrad Inner product of two tensors
- Rick16
- · Replies 6 ·
Undergrad Question about Gradient's Domain and Range
- littlemathquark
- · Replies 6 ·
Graduate Understanding: double of conformally flat manifold is conformally flat
- kappaka
- · Replies 1 ·
Undergrad How to find inverse coordinates?
- Rick16
- · Replies 7 ·
Undergrad The Road to Reality - exercise on scalar product
- cianfa72
- · Replies 36 ·
Undergrad Trying to learn tensor algebra
- Rick16
- · Replies 8 ·
Undergrad Notion of congruent curve along a vector field
- cianfa72
- · Replies 1 ·
Undergrad Dirichlet problem boundary conditions
- cianfa72
- · Replies 4 ·
Undergrad Which basis-forms are pseudo-tensors?
- SiennaTheGr8
- · Replies 3 ·
Graduate Alternative topology of our 3D space
- kochanskij
- · Replies 1 ·
Undergrad Manifold hypersurface foliation and Frobenius theorem
- cianfa72
- · Replies 73 ·
Undergrad SL(n,R) Lie group as submanifold of GL(n,R)
- cianfa72
- · Replies 36 ·
Undergrad Grassmannian as smooth manifold
- Korybut
- · Replies 6 ·
Undergrad Can covariant derivative tensorialness be derived?
- Pencilvester
- · Replies 18 ·
Undergrad Frobenius theorem applied to frame fields
- cianfa72
- · Replies 30 ·
Undergrad 2-sphere manifold intrinsic definition
- cianfa72
- · Replies 44 ·
Undergrad Radius of curvature formula when the denominator = 0
- nomadreid
- · Replies 18 ·
Undergrad Quotient law and the curl in index notation
- SiennaTheGr8
- · Replies 1 ·
Undergrad What is the difference between Gaussian and sectional curvature?
- PhysicsRock
- · Replies 1 ·
Undergrad Do gradient and curl only differ by a Levi-Cavita tensor?
- FQVBSina_Jesse
- · Replies 23 ·
High School Hopf fibration, Bloch sphere and quantum rotations - interactive site
- vladramen
- · Replies 1 ·
Undergrad 3-parameter group of symmetries on the plane
- cianfa72
- · Replies 51 ·
Undergrad Approximating smooth curved manifolds with "local bits" of curvature?
- Spinnor
- · Replies 5 ·
Undergrad Conformal flatness of ellipsoid
- ergospherical
- · Replies 0 ·
Undergrad Flat surface to curved surface
- anilswipe
- · Replies 4 ·
Undergrad Definition of manifolds with boundary
- PhysicsRock
- · Replies 3 ·
Undergrad When can I commute the 4-gradient and the "space-time" integral?
- tannhaus
- · Replies 2 ·
Undergrad Spherical trig - sphere radius from 6 lengths
- Vanadium 50
- · Replies 8 ·
Undergrad Identification tangent bundle over affine space with product bundle
- cianfa72
- · Replies 13 ·
Undergrad Induced orientation on boundary of ##\mathbb{H}^n## in ##\mathbb{R}^n##
- PhysicsRock
- · Replies 6 ·
Undergrad Resources on the Derivation of generalized Stokes' theorem
- PhysicsRock
- · Replies 11 ·
Graduate How to switch from tensor products to wedge product
- victorvmotti
- · Replies 5 ·
Undergrad A way to comprehend the geometry of a hypercube
- Warp
- · Replies 2 ·
High School What would need to be possible to make a cube of circles?
- SheldonCooper13
- · Replies 4 ·
Undergrad Degrees of Freedom in Lagrangian Mechanics for a Fractal Path
- Pikkugnome
- · Replies 2 ·
Undergrad Is Diagrammatic Tensor Notation Widely Used in Mathematics?
- Hill
- · Replies 33 ·
Graduate 3-connection on nontrivial topological 3-manifold
- polology
- · Replies 11 ·
Undergrad Question regarding the 3-form ##dx^i \wedge dx^j \wedge dx^k##
- PhysicsRock
- · Replies 13 ·
Undergrad Converse of focus-directrix property of conic sections
- arham_jain_hsr
- · Replies 2 ·
Undergrad I need help generating a 2D representation of a curved plane
- OlarFin
- · Replies 5 ·
Undergrad Short question about principal bundle
- Korybut
- · Replies 9 ·
Undergrad Definition of tangent vector on smooth manifold
- cianfa72
- · Replies 21 ·
Undergrad How to apply tensor transformation rule
- guv
- · Replies 9 ·
Graduate What subset of a 3D space can be addressed by a single chart?
- gnnmartin
- · Replies 10 ·
Undergrad Frobenius theorem for differential one forms
- cianfa72
- · Replies 6 ·
Undergrad Dirac delta function in 2d polar coordinates
- Trollfaz
- · Replies 4 ·
Graduate Differential structure of the group of automorphism of a Lie group
- padawan
- · Replies 0 ·
Undergrad Invariance of a tensor of order 2
- Thytanium
- · Replies 2 ·
Graduate What Is the Gauss Embedding Theorem Mentioned in the Video Talk?
- The Tortoise-Man
- · Replies 1 ·
Undergrad Help with Differential Forms - self wedge product terms
- thatboi
- · Replies 13 ·
Undergrad Rewriting Equation of Motion in terms of Dual Fields (Chern-Simons)
- thatboi
- · Replies 2 ·
Undergrad Contact manifold and Darboux's theorem
- cianfa72
- · Replies 14 ·
Undergrad Differential operator vs one-form (covector field)
- cianfa72
- · Replies 10 ·
High School East-West error at regular points on the Azimuthal Equidistant Map
- Miles Behind
- · Replies 3 ·
Undergrad How do I parametrize a conical/cylindrical surface in cylindrical unit vectors?
- Trollfaz
- · Replies 7 ·
Undergrad How can a sphere be transformed using differential geometry?
- James1355
- · Replies 17 ·
Undergrad Miller indices and periodic boundary conditions
- Spathi
- · Replies 0 ·
Undergrad Trouble with metric. Holonomic basis and the normalised basis
- GR191511
- · Replies 6 ·
Undergrad Also in 3D, two reflections make a rotation?
- nomadreid
- · Replies 2 ·
High School How to find the infinitesimal coordinate transform along a hyperbola?
- Sciencemaster
- · Replies 1 ·
Graduate Tensor/Vector decomposition/representation & DOF arguement
- binbagsss
- · Replies 2 ·