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 Vector Fields and Vector Bundles

  • AiRAVATA
  • · Replies 7 ·
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7

Graduate Transformations taking straight lines to straight lines

  • Palindrom
  • · Replies 5 ·
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5

Graduate Surface Definition from Pressley's "Elementary Differential Geometry

  • quasar987
  • · Replies 9 ·
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9

Graduate How Does a 2-Form Act on Vector Fields X,Y?

  • SeReNiTy
  • · Replies 3 ·
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3

Graduate How Do Tensors Enhance Problem Solving in Forums?

  • stephen_weber
  • · Replies 1 ·
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1

Graduate Parallel Translation in R^3 & S^2: Contradiction?

  • Palindrom
  • · Replies 9 ·
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9

Graduate Do All Smooth Manifolds Admit a Complete Riemannian Metric?

  • mtiano
  • · Replies 1 ·
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1

Graduate Explore Geometry of Symmetric Spaces & Lie Groups on PF

  • garrett
  • · Replies 122 ·
5
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Graduate Where to find notes onTensor Analysis or Differential Geometry.

  • Nusc
  • · Replies 1 ·
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1

Graduate Equidistant Points on a Sphere: What is the Series and How to Draw Efficiently?

  • ChemistryInclined
  • · Replies 3 ·
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3

Graduate Dual Space Topology: A to B Inclusion Map

  • kakarukeys
  • · Replies 9 ·
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9

Graduate What is the proof for the distance formula from a point to a plane?

  • Reshma
  • · Replies 5 ·
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5

Graduate Curve of intersection of plane and surface

  • Yura
  • · Replies 9 ·
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9

Graduate Geodesic Curvature (Curvature of a curve)

  • Reality_Patrol
  • · Replies 8 ·
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8

Undergrad Find Equations for Point #3 on a Line in 3D Space

  • ronatu
  • · Replies 2 ·
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2

Graduate What is the relationship between Ricci and K in two dimensions?

  • stephen_weber
  • · Replies 12 ·
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12

Graduate Question and answer on 'not exact' forms

  • precondition
  • · Replies 2 ·
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2

Graduate Relationship between tensors

  • sparkster
  • · Replies 1 ·
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1

Graduate In which frame does the unit 2-sphere look locally flat?

  • masudr
  • · Replies 3 ·
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3

Graduate Fundamental Group: Combining Loops

  • waht
  • · Replies 14 ·
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14

Graduate Proving the Relation Between Weyl Tensor, Ricci Tensor & Scalar

  • sroeyz
  • · Replies 3 ·
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3

Graduate Cartan forms and structure equations

  • precondition
  • · Replies 2 ·
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2

Graduate Meaning of integrating exterior forms

  • KamYi
  • · Replies 2 ·
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2

Graduate I thought w(f) where w=dual vector f=vector is Reals?

  • precondition
  • · Replies 1 ·
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1

Graduate Proving Topological Space L is Locally Homeomorphic to R but not Hausdorff

  • AiRAVATA
  • · Replies 3 ·
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3

Graduate Why Must the Projection Function in Fiber Bundles Have a Specific Form?

  • mma
  • · Replies 17 ·
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17

Undergrad Problem with polynomials and spheres

  • markcholden
  • · Replies 1 ·
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1

Graduate Coordinates in Riemannian Geometry

  • KalyanK
  • · Replies 1 ·
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1

Graduate Connected set and regular boundaries

  • rdabra
  • · Replies 1 ·
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1

Graduate Transforming to curved manifolds

  • masudr
  • · Replies 4 ·
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4

Graduate ICM 2006 Fields Winners: Perelman, Tao, Okounkov, Werner Laudatio Talks

  • marcus
  • · Replies 28 ·
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28

Undergrad Intro to tensors book for self-study?

  • Mothrog
  • · Replies 5 ·
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5

Graduate What are some tips for finding geodesics on a surface in R^3?

  • Feles Cestriana
  • · Replies 4 ·
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4

Graduate Perelman, Poincare Conjecture solved now?

  • Clausius2
  • · Replies 6 ·
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6

Graduate Geometrical methods of mathematical physics

  • pmb_phy
  • · Replies 3 ·
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3

Undergrad Quadlateration Trilateration formula

  • insolace
  • · Replies 1 ·
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1

Graduate How Does Discretizing a Smooth Manifold Affect Its Geometric Properties?

  • lokofer
  • · Replies 2 ·
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2

Undergrad Electric and magnetic constants are tensors

  • dervast
  • · Replies 50 ·
2
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50

Graduate Proving Homeomorphism is a Diffeomorphism | Riemannian Geometry

  • sroeyz
  • · Replies 2 ·
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2

Graduate Complete Solution of Poincare Conjecture

  • selfAdjoint
  • · Replies 9 ·
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9

Graduate Understanding the Formulas for Area of Spherical Triangles

  • denni89627
  • · Replies 2 ·
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2

Graduate Why we have to definte covariant derivative?

  • HeilPhysicsPhysics
  • · Replies 4 ·
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4

Graduate What is the metric tensor on a spherical surface?

  • HeilPhysicsPhysics
  • · Replies 2 ·
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2

Graduate What is the metric (distance function) on the 1-sphere and 2-sphere?

  • SeReNiTy
  • · Replies 2 ·
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2

Graduate Derivation Of The Faraday Two-Form

  • ObsessiveMathsFreak
  • · Replies 5 ·
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5

Graduate Structure constants of Lie algebra

  • marton
  • · Replies 3 ·
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3

Graduate Differential geometry lecture notes

  • franznietzsche
  • · Replies 17 ·
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17

Graduate What is the Correct Metric Tensor for the Unit Sphere?

  • quasar987
  • · Replies 3 ·
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3

Graduate Studying Spivak: Calculus on Manifolds & Diff Geom, Worth It?

  • SeReNiTy
  • · Replies 4 ·
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4

Graduate Lie group, Riemannian metric, and connection

  • marton
  • · Replies 2 ·
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2

Graduate Vectors, one-forms and gradients

  • Neoma
  • · Replies 71 ·
3
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Graduate Can basis covectors be defined without a metric?

  • masudr
  • · Replies 19 ·
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19

Graduate Riemannian volume form without local coordinates

  • Don Aman
  • · Replies 10 ·
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10

Graduate Understanding Continuity on Manifolds

  • pmb_phy
  • · Replies 28 ·
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28

Graduate Is Symmetry Present in the Derivatives of Normal Vectors on Surfaces?

  • rych
  • · Replies 3 ·
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3

Graduate Exterior Derivative: A Visual Explanation

  • KarateMan
  • · Replies 2 ·
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2

Undergrad Equation of a Helix: Find Answers to Parametric Equations

  • NEWO
  • · Replies 1 ·
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1

Graduate Where can I find free or affordable resources for learning Reimann Geometry?

  • mepcotterell
  • · Replies 5 ·
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5

Graduate Contraction of Curvature 2-Form for Calculating Ricci Tensor and Einstein Tensor

  • Oxymoron
  • · Replies 4 ·
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4

Undergrad What is the Spherical Coordinate Equivalent of the Cartesian k Unit Vector?

  • pivoxa15
  • · Replies 4 ·
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4

Graduate What is the One Form Needed for Div and Curl in 3-Space?

  • SeReNiTy
  • · Replies 2 ·
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2

Graduate Linearly Independent Killing Fields in n-D Manifold

  • Cexy
  • · Replies 6 ·
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6

Graduate Inverse function of a function of two variables

  • closet mathemetician
  • · Replies 1 ·
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1

Graduate Geodesics in Minkowski Spacetime

  • Oxymoron
  • · Replies 2 ·
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2

Graduate Is the Special Linear Group a Submanifold of the Space of Matrices?

  • cmiller5277
  • · Replies 6 ·
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6

Graduate Covariant derivative of the gradient

  • eljose
  • · Replies 1 ·
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1

Graduate How A Threesphere Would Look or Work?

  • Silverbackman
  • · Replies 7 ·
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7

Graduate Rank condition in the Implicit Mapping Theorm

  • cmiller5277
  • · Replies 3 ·
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3

Graduate Schwarzschild Solution using Cartan's Formalism

  • Oxymoron
  • · Replies 3 ·
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3

Graduate How Do You Determine Basis Vectors for the Tangent Space of a Surface in R^4?

  • Alteran
  • · Replies 6 ·
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6

Graduate Can we pullback and pushforward vector fields and functions on manifolds?

  • Oxymoron
  • · Replies 7 ·
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7

Graduate Can Lie Algebra Structures Be Extended to Tangent Spaces Near the Identity?

  • Pietjuh
  • · Replies 1 ·
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1

Graduate Various problems concerning Exterior calculus

  • Oxymoron
  • · Replies 17 ·
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17

Graduate Why Is the Exterior Derivative Only Defined on Differential Forms in a Manifold?

  • Oxymoron
  • · Replies 6 ·
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6

Undergrad Why Study Tensor Analysis? Benefits & History

  • sara_math
  • · Replies 18 ·
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18

Graduate Proving an Identity from Differential Geometry

  • mannyfold
  • · Replies 4 ·
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4

Graduate Way to express a general vector field

  • 0rthodontist
  • · Replies 2 ·
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2

Graduate Differential Geometry/Ricci Calculus Question

  • mannyfold
  • · Replies 6 ·
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6

Graduate One-form is a linear map from a vector to a real number

  • jwsiii
  • · Replies 15 ·
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15

Undergrad What is the relationship between wedge product and cross product?

  • closet mathemetician
  • · Replies 2 ·
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2

Graduate Why Must We Contract Two Indices to Form the Ricci Tensor?

  • Oxymoron
  • · Replies 8 ·
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8

Graduate Who discovered the general case of Stokes' Theorem?

  • DeadWolfe
  • · Replies 10 ·
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10

Graduate Explicit or analytic formula for a homeomorphism

  • sparkster
  • · Replies 2 ·
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2

Graduate 4 dimensional spacetime manifold question

  • closet mathemetician
  • · Replies 7 ·
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7

Graduate Differential Forms vs. Directed Measures

  • kryptyk
  • · Replies 19 ·
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19

Graduate What Does 'Vanishes Identically' Mean in Mathematical Context?

  • Ratzinger
  • · Replies 1 ·
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1

Graduate Particle moves in a plane, and i've found that x.n=k

  • jackbauer
  • · Replies 1 ·
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1

Undergrad Find (x,y) of a Point on an Ellipse Given Foci and Radii Info

  • Crusty
  • · Replies 2 ·
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2

Graduate Is the Scalar \( R^{ji} R_{ij} - R^2 \) Recognized in Mathematical Physics?

  • joschu
  • · Replies 5 ·
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5

Graduate What are the Spherical Interior Angles for Regular and Archimedean Solids?

  • RandallB
  • · Replies 11 ·
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11

Graduate What objects, in General Relativity, carry units?

  • pensano
  • · Replies 3 ·
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3

Graduate Riemannian Manifolds: Metric Structures for Topological Spaces

  • Ratzinger
  • · Replies 16 ·
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16

Graduate Acceleration Tensor - Rotating Frame

  • PrinceOfDarkness
  • · Replies 3 ·
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3

Graduate What is the result of multiplying a matrix by the divergence of a vector?

  • mkkrnfoo85
  • · Replies 2 ·
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2

Graduate Can Analytic Continuation Determine the Metric Over a 4-D Manifold?

  • straycat
  • · Replies 18 ·
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18

Graduate Introduction to Differential Geometry

  • JasonRox
  • · Replies 28 ·
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28

Graduate Inverse of the Stereographic Projection

  • CMoore
  • · Replies 5 ·
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5

Graduate How Can Isomorphic Tangent Spaces Help Understand Derivations?

  • CMoore
  • · Replies 3 ·
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3

Graduate Noncoordinate Basis: Explanation and Importance

  • matness
  • · Replies 17 ·
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17

Graduate What is the second fundamental form?

  • the.bone
  • · Replies 5 ·
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5