Differential Geometry Forum

Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.

Threads

Graduate On covariance of the Lagrange equations

  • wrobel
  • · Replies 1 ·
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1

Undergrad Do non-orthogonal coordinate systems mean dependent coordinates?

  • gmmaro
  • · Replies 8 ·
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8

Graduate Nonautonomous Lie derivative

  • wrobel
  • · Replies 0 ·
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0

Graduate Equivalent definitions of tensor field

  • cianfa72
  • · Replies 5 ·
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5

Graduate Strain Tensor Based on Clifford Algebra

  • Arash1950
  • · Replies 3 ·
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3

Undergrad Differential Geometry with GNU/Linux

  • diegogarcia
  • · Replies 9 ·
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9

Undergrad About the maximal extension of local charts on a manifold

  • cianfa72
  • · Replies 8 ·
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8

Graduate Injective immersion and embedding

  • Korybut
  • · Replies 2 ·
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2

Undergrad Get geodesics & parallel transport on 2D surfaces (discrete timestep)

  • Tachytaenius
  • · Replies 12 ·
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12

Undergrad Compact manifold cannot be represented by (single) parametric equation

  • elias001
  • · Replies 5 ·
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5

Undergrad ##C^{\infty}##-module of smooth vector fields can lack a basis

  • cianfa72
  • · Replies 9 ·
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9

Undergrad Round 3-sphere symmetries as subspace of 4D Euclidean space

  • cianfa72
  • · Replies 6 ·
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6

Undergrad Differential structures over a topological manifold

  • cianfa72
  • · Replies 4 ·
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4

Undergrad ##SO(3)## topology

  • cianfa72
  • · Replies 29 ·
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29

Undergrad Pseudo-Riemaniann isometries

  • cianfa72
  • · Replies 4 ·
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4

Undergrad Spherically symmetric manifold

  • cianfa72
  • · Replies 10 ·
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10

Undergrad Smooth Manifold Chart Lemma

  • cianfa72
  • · Replies 4 ·
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4

Undergrad Vector fields wedge product vs covector field

  • cianfa72
  • · Replies 11 ·
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11

Undergrad Definition of a Manifold

  • littlemathquark
  • · Replies 15 ·
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15

Undergrad Chain Rule (partial derivatives): basic interpretation question

  • nomadreid
  • · Replies 5 ·
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5

Undergrad Definition of inertia tensor from a differential geometry viewpoint

  • cianfa72
  • · Replies 15 ·
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15

Undergrad Closed implies exact (differential 1-forms on R^2)

  • PhDeezNutz
  • · Replies 6 ·
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6

Undergrad Transformation of second rank tensor

  • LightPhoton
  • · Replies 4 ·
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4

Undergrad Differential structure on topological manifolds of dimension <= 3

  • cianfa72
  • · Replies 11 ·
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11

Undergrad Maximal atlas of topological manifold

  • cianfa72
  • · Replies 37 ·
2
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37

Undergrad Galilean spacetime as a fiber bundle

  • cianfa72
  • · Replies 16 ·
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16

Undergrad 2-sphere with any topology can't be homeomorphic to the plane

  • cianfa72
  • · Replies 5 ·
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5

Undergrad Must a Smooth Section Over a Mobius Strip Take Value Zero at Some Point?

  • cianfa72
  • · Replies 8 ·
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8

Undergrad Properties of the initial topology from a topological manifold

  • cianfa72
  • · Replies 8 ·
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8

Graduate Bachman : A geometric approach to differential forms

  • mrslamovics
  • · Replies 2 ·
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2

Undergrad Poincare lemma for one-form on ##\mathbb R^2 \backslash \{ 0 \}##

  • cianfa72
  • · Replies 15 ·
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15

High School Axes on a hyperbolic plane

  • BerryGo
  • · Replies 4 ·
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4

Undergrad On the definition of canonical coordinates in phase space

  • cianfa72
  • · Replies 9 ·
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9

Undergrad Confused about the inner product

  • Rick16
  • · Replies 58 ·
2
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58

Undergrad Induced metric in general case

  • gerald V
  • · Replies 1 ·
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1

Undergrad Dot product between basis vectors and dual basis vectors

  • Rick16
  • · Replies 17 ·
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17

Graduate Is the Lie derivative a tensor itself?

  • spinless
  • · Replies 4 ·
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4

Undergrad Is there a consensus about the meaning of the Christoffel symbols' indices?

  • Rick16
  • · Replies 2 ·
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2

Undergrad Help with area formula using direction cosines

  • davidwinth
  • · Replies 3 ·
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3

Undergrad Inner product of two tensors

  • Rick16
  • · Replies 6 ·
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6

Undergrad Question about Gradient's Domain and Range

  • littlemathquark
  • · Replies 6 ·
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6

Graduate Understanding: double of conformally flat manifold is conformally flat

  • kappaka
  • · Replies 1 ·
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1

Undergrad How to find inverse coordinates?

  • Rick16
  • · Replies 7 ·
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7

Undergrad The Road to Reality - exercise on scalar product

  • cianfa72
  • · Replies 36 ·
2
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36

Undergrad Trying to learn tensor algebra

  • Rick16
  • · Replies 8 ·
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8

Undergrad Notion of congruent curve along a vector field

  • cianfa72
  • · Replies 1 ·
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1

Undergrad Dirichlet problem boundary conditions

  • cianfa72
  • · Replies 4 ·
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4

Undergrad Which basis-forms are pseudo-tensors?

  • SiennaTheGr8
  • · Replies 3 ·
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3

Graduate Alternative topology of our 3D space

  • kochanskij
  • · Replies 1 ·
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1

Undergrad Manifold hypersurface foliation and Frobenius theorem

  • cianfa72
  • · Replies 73 ·
3
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73

Undergrad SL(n,R) Lie group as submanifold of GL(n,R)

  • cianfa72
  • · Replies 36 ·
2
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36

Undergrad Grassmannian as smooth manifold

  • Korybut
  • · Replies 6 ·
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6

Undergrad Can covariant derivative tensorialness be derived?

  • Pencilvester
  • · Replies 18 ·
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18

Undergrad Frobenius theorem applied to frame fields

  • cianfa72
  • · Replies 30 ·
2
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30

Undergrad 2-sphere manifold intrinsic definition

  • cianfa72
  • · Replies 44 ·
2
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44

Undergrad Radius of curvature formula when the denominator = 0

  • nomadreid
  • · Replies 18 ·
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18

Undergrad Quotient law and the curl in index notation

  • SiennaTheGr8
  • · Replies 1 ·
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1

Undergrad What is the difference between Gaussian and sectional curvature?

  • PhysicsRock
  • · Replies 1 ·
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1

Undergrad Do gradient and curl only differ by a Levi-Cavita tensor?

  • FQVBSina_Jesse
  • · Replies 23 ·
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23

High School Hopf fibration, Bloch sphere and quantum rotations - interactive site

  • vladramen
  • · Replies 1 ·
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1

Undergrad 3-parameter group of symmetries on the plane

  • cianfa72
  • · Replies 51 ·
2
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51

Undergrad Approximating smooth curved manifolds with "local bits" of curvature?

  • Spinnor
  • · Replies 5 ·
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5

Undergrad Conformal flatness of ellipsoid

  • ergospherical
  • · Replies 0 ·
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0

Undergrad Flat surface to curved surface

  • anilswipe
  • · Replies 4 ·
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4

Undergrad Definition of manifolds with boundary

  • PhysicsRock
  • · Replies 3 ·
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3

Undergrad When can I commute the 4-gradient and the "space-time" integral?

  • tannhaus
  • · Replies 2 ·
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2

Undergrad Spherical trig - sphere radius from 6 lengths

  • Vanadium 50
  • · Replies 8 ·
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8

Undergrad Identification tangent bundle over affine space with product bundle

  • cianfa72
  • · Replies 13 ·
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13

Undergrad Induced orientation on boundary of ##\mathbb{H}^n## in ##\mathbb{R}^n##

  • PhysicsRock
  • · Replies 6 ·
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6

Undergrad Resources on the Derivation of generalized Stokes' theorem

  • PhysicsRock
  • · Replies 11 ·
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11

Graduate How to switch from tensor products to wedge product

  • victorvmotti
  • · Replies 5 ·
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5

Undergrad A way to comprehend the geometry of a hypercube

  • Warp
  • · Replies 2 ·
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2

High School What would need to be possible to make a cube of circles?

  • SheldonCooper13
  • · Replies 4 ·
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4

Undergrad Degrees of Freedom in Lagrangian Mechanics for a Fractal Path

  • Pikkugnome
  • · Replies 2 ·
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2

Undergrad Is Diagrammatic Tensor Notation Widely Used in Mathematics?

  • Hill
  • · Replies 33 ·
2
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33

Graduate 3-connection on nontrivial topological 3-manifold

  • polology
  • · Replies 11 ·
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11

Undergrad Question regarding the 3-form ##dx^i \wedge dx^j \wedge dx^k##

  • PhysicsRock
  • · Replies 13 ·
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13

Undergrad Converse of focus-directrix property of conic sections

  • arham_jain_hsr
  • · Replies 2 ·
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2

Undergrad I need help generating a 2D representation of a curved plane

  • OlarFin
  • · Replies 5 ·
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5

Undergrad Short question about principal bundle

  • Korybut
  • · Replies 9 ·
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9

Undergrad Definition of tangent vector on smooth manifold

  • cianfa72
  • · Replies 21 ·
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21

Undergrad How to apply tensor transformation rule

  • guv
  • · Replies 9 ·
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9

Graduate What subset of a 3D space can be addressed by a single chart?

  • gnnmartin
  • · Replies 10 ·
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10

Undergrad Frobenius theorem for differential one forms

  • cianfa72
  • · Replies 6 ·
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6

Undergrad Dirac delta function in 2d polar coordinates

  • Trollfaz
  • · Replies 4 ·
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4

Graduate Differential structure of the group of automorphism of a Lie group

  • padawan
  • · Replies 0 ·
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0

Undergrad Invariance of a tensor of order 2

  • Thytanium
  • · Replies 2 ·
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2

Graduate What Is the Gauss Embedding Theorem Mentioned in the Video Talk?

  • The Tortoise-Man
  • · Replies 1 ·
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1

Undergrad Help with Differential Forms - self wedge product terms

  • thatboi
  • · Replies 13 ·
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13

Undergrad Rewriting Equation of Motion in terms of Dual Fields (Chern-Simons)

  • thatboi
  • · Replies 2 ·
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2

Undergrad Contact manifold and Darboux's theorem

  • cianfa72
  • · Replies 14 ·
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14

Undergrad Differential operator vs one-form (covector field)

  • cianfa72
  • · Replies 10 ·
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10

High School East-West error at regular points on the Azimuthal Equidistant Map

  • Miles Behind
  • · Replies 3 ·
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3

Undergrad How do I parametrize a conical/cylindrical surface in cylindrical unit vectors?

  • Trollfaz
  • · Replies 7 ·
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7

Undergrad How can a sphere be transformed using differential geometry?

  • James1355
  • · Replies 17 ·
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17

Undergrad Miller indices and periodic boundary conditions

  • Spathi
  • · Replies 0 ·
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0

Undergrad Trouble with metric. Holonomic basis and the normalised basis

  • GR191511
  • · Replies 6 ·
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6

Undergrad Also in 3D, two reflections make a rotation?

  • nomadreid
  • · Replies 2 ·
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2

High School How to find the infinitesimal coordinate transform along a hyperbola?

  • Sciencemaster
  • · Replies 1 ·
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1

Graduate Tensor/Vector decomposition/representation & DOF arguement

  • binbagsss
  • · Replies 2 ·
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2