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 Bonnet Transformation: Explaining the Alpha-Helix to Beta Barrel Transition

  • akoska
  • · Replies 1 ·
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Graduate Can Geodesics Be Inflectional in Euclidean Space?

  • humanino
  • · Replies 3 ·
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3

Undergrad Vector or Not Vector: Analysis of Magnitude & Direction

  • BobbyFluffyPric
  • · Replies 42 ·
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Graduate How to get the normal bivector to a surface?

  • HolyPhia
  • · Replies 2 ·
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2

Graduate Please me to understand Einstein notation and permutations

  • Tiggy
  • · Replies 1 ·
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Graduate WHY there is no scalar equation for a line in three dimensions ?

  • Rosicky08
  • · Replies 7 ·
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7

Graduate What is the Equation of the Ellipse in 3D for Magnetic Field Visualization?

  • Klaws
  • · Replies 11 ·
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11

Graduate Proving Stokes Theorem: The Intuition and Application

  • Terilien
  • · Replies 4 ·
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4

Graduate From Christoffel symbols to connection 1-forms

  • cosmicstring1
  • · Replies 12 ·
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12

Graduate That given a continuous surface, contour lines exist

  • JamesTheBond
  • · Replies 6 ·
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6

Graduate Connection coefficients entering differential operators

  • masudr
  • · Replies 1 ·
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Undergrad Circumscribing a sphere with a tetrahedron

  • DaveC426913
  • · Replies 8 ·
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8

Graduate Bivectors/Trivectors: How to imagine?

  • Swapnil
  • · Replies 7 ·
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7

Graduate Can the Laplacian of a Scalar Field be Considered as its Curvature?

  • Swapnil
  • · Replies 2 ·
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Graduate Riemann-Tensor have in n- dimensional space?

  • Thaakisfox
  • · Replies 5 ·
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5

Graduate Is the 'distance function' the same as the 'metric' in physics texts?

  • pmb_phy
  • · Replies 35 ·
2
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Graduate Geodesics and the Action Principle

  • AiRAVATA
  • · Replies 3 ·
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3

Graduate Original motivation of differential geometry

  • Terilien
  • · Replies 25 ·
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25

Graduate Hypervolume of a Hypercube in Minkowski Space

  • MeJennifer
  • · Replies 11 ·
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11

Graduate Need help with Christoffel symbols? Here are some examples to practice with!

  • Terilien
  • · Replies 7 ·
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7

Graduate Killing Vector Fields: Generating Local Transformations?

  • kakarukeys
  • · Replies 3 ·
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3

Undergrad Axes of an ellipse. I on this

  • sutupidmath
  • · Replies 2 ·
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2

Graduate Tensor products and tensor algebras

  • asub
  • · Replies 1 ·
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1

Graduate Recommendations for diff geom. textbook

  • AlphaNumeric
  • · Replies 17 ·
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17

Graduate Uncovering the Mystery of Covariant Derivatives: Sean Carroll's Perspective

  • Terilien
  • · Replies 12 ·
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12

Graduate Differential of lin. transformation between vector spaces

  • cliowa
  • · Replies 17 ·
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17

Graduate Helmholtz Theorem on Decomposition of Vectors

  • Gonçalo
  • · Replies 1 ·
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1

Graduate Searching for a point in space

  • JoAuSc
  • · Replies 2 ·
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2

Graduate Understanding RP^n and CP^n: Geometric Projective Spaces

  • AlphaNumeric
  • · Replies 4 ·
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4

Graduate Simply Connected and Fundamental Group

  • waht
  • · Replies 2 ·
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2

High School Problem on tangents to a cirlce

  • anantchowdhary
  • · Replies 8 ·
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8

Undergrad Calculating Minimum Distance Between Two Co-ordinates on Earth

  • lbass
  • · Replies 2 ·
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2

Graduate Differential geometry recommendations

  • Terilien
  • · Replies 2 ·
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2

Graduate Why do two lines have to be 'great circles' on a sphere?

  • bjgawp
  • · Replies 5 ·
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5

Graduate How to FULLY understand a definition?

  • andytoh
  • · Replies 30 ·
2
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Undergrad I have difficulty in visualizing the divergence of vector fields.

  • hanson
  • · Replies 2 ·
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2

Graduate Tensor Product: Basis for Higher Order Tensors and Its Proof

  • Terilien
  • · Replies 37 ·
2
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37

Graduate Which Book on Riemannian Geometry Balances Intuition and Minimal Prerequisites?

  • Ragnar
  • · Replies 35 ·
2
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Graduate The tensor product and its motivation

  • Terilien
  • · Replies 3 ·
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3

Undergrad What Curve Results from the Centers of Perpendicular Lines to an Ellipse?

  • transgalactic
  • · Replies 7 ·
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7

Graduate Calculating Metric/Metric Tensor for Curved Spaces

  • marcusesses
  • · Replies 1 ·
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1

Undergrad Gaussian Geometry: Finding Resources Online

  • Terilien
  • · Replies 2 ·
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2

Graduate Lie dragging a vector around the ellipse

  • wandering.the.cosmos
  • · Replies 5 ·
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5

Graduate Kronecker Delta: A Relativity and Tensor Explanation

  • Terilien
  • · Replies 5 ·
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5

Graduate How Can I Prove This Metric is Flat?

  • astronomia84
  • · Replies 16 ·
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16

Undergrad Tensor Product Explained - Examples Included

  • Ragnar
  • · Replies 1 ·
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1

Graduate How do I calculate the volume of a hypercylindrical shape in n dimensions?

  • americanforest
  • · Replies 3 ·
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3

Graduate From Simple Groups to Quantum Field Theory

  • Mehdi_
  • · Replies 43 ·
2
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Graduate Lie vs Covariant Derivative: Intuitive Understanding

  • sit.think.solve
  • · Replies 3 ·
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Graduate Hello,I am doing a project on Riemann, but. .

  • pibomb
  • · Replies 8 ·
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8

Graduate Understanding the Metric Tensor in General Relativity

  • Ragnar
  • · Replies 3 ·
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3

Undergrad Intersection of two 3D parametric curves

  • Quaoar
  • · Replies 4 ·
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4

Undergrad Schaum's Outline: Tensor Calculus Intro Basics

  • Ragnar
  • · Replies 1 ·
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1

Graduate How Can Infinite Subcovers Exist in Compact Spaces Without Contradiction?

  • quantum123
  • · Replies 5 ·
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5

Graduate What are the general equations of geodesics on a cylinder's surface?

  • tehno
  • · Replies 11 ·
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11

Graduate Deriving a Small Circle Equation in Spherical Coordinates: Any Pointers?

  • whatta
  • · Replies 1 ·
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1

Graduate Definition of differentiability on a manifold

  • quasar987
  • · Replies 15 ·
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15

Undergrad Help needed - Equation of a wedge shaped plane

  • stu807
  • · Replies 4 ·
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4

Graduate Can a Surface in R³ Have This Prescribed Riemannian Metric?

  • KarstenKarsten
  • · Replies 6 ·
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6

Graduate Understanding Tensor Components: The Role of Index Order in Vector Spaces

  • quasar987
  • · Replies 4 ·
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4

Undergrad Understanding Stoke's Theorem: Does Surface Integral Depend on Shape?

  • nolanp2
  • · Replies 2 ·
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2

Graduate Covariant and Contravariant: What Are the Differences in Differential Geometry?

  • StatusX
  • · Replies 62 ·
3
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62

Graduate Curl of Function: Constant Magnitude or Way Off?

  • nolanp2
  • · Replies 5 ·
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5

Graduate Linear transition maps on manifolds

  • vanesch
  • · Replies 7 ·
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7

Graduate Where Am I Going Wrong with Kahler Metric Computations?

  • AlphaNumeric
  • · Replies 1 ·
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1

Graduate Proving the Mapping f:S^2\times \mathbb{R} \rightarrow S^2

  • cristo
  • · Replies 7 ·
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7

Graduate What Does \partial_{[\mu}\omega_{\nu]} Mean?

  • Jheriko
  • · Replies 13 ·
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13

Graduate Covariant and Contravariant Rank-2 Tensors

  • Truth Finder
  • · Replies 2 ·
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2

Graduate Which Textbook Best Teaches Tensor Analysis for General Relativity?

  • Nusc
  • · Replies 31 ·
2
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31

Graduate Pointcare Conjecture - Grigory Perelman's Proof

  • Chaos' lil bro Order
  • · Replies 2 ·
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2

Graduate Lagrange equations with constraints

  • r4nd0m
  • · Replies 3 ·
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3

Graduate Proving Sphere has Minimal Surface Area for Volume

  • pivoxa15
  • · Replies 2 ·
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2

Graduate Proving Cartan's Identity: Tips & Hints

  • SeReNiTy
  • · Replies 3 ·
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3

Graduate Differential Forms & the Star Operator

  • leon1127
  • · Replies 1 ·
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1

Graduate Spherical-esque Coordiante System

  • LeBrad
  • · Replies 4 ·
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4

Graduate Help on Contraction: Proving i_v(\omega_1 \wedge \omega_2)

  • AiRAVATA
  • · Replies 4 ·
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4

Graduate Proving Decomposability of Forms in Spivak's Book (Vol. 1, Chap. 7)

  • AiRAVATA
  • · Replies 1 ·
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1

Undergrad Understanding Tensors for Beginners in Special Relativity

  • aeroboyo
  • · Replies 16 ·
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16

Graduate My Solutions to Tensors and Manifolds

  • andytoh
  • · Replies 1 ·
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1

Graduate How Do Complex Eigenvalues Affect Numerical Solutions of PDE Systems?

  • desA
  • · Replies 2 ·
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2

Graduate Book on tensor symmetry, geometries, surfaces

  • desA
  • · Replies 2 ·
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2

Graduate How Do Isometries of the n-Torus Relate to R^n?

  • Palindrom
  • · Replies 3 ·
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3

Graduate Noncoordinate basis vector fields

  • desic
  • · Replies 1 ·
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1

Graduate Hypersurfaces with vanishing extrinsic curvature

  • arild
  • · Replies 3 ·
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3

Graduate Who is the author of Differential Forms book?

  • acm
  • · Replies 5 ·
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5

Graduate Theorem of Curves in higher dimensions

  • eddo
  • · Replies 8 ·
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8

Graduate Levi-civita permutation tensor, and kroneker delta

  • Divisionbyzer0
  • · Replies 6 ·
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6

Graduate Index Transformation: Understanding Notation & Index Rules

  • Peregrine
  • · Replies 3 ·
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3

Graduate Tangent space, derivation defifinition

  • mrandersdk
  • · Replies 8 ·
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8

Graduate Understanding Index Notation in Tensor Calculus?

  • Peregrine
  • · Replies 5 ·
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5

Graduate Gradients of Vectors and Dyadic Products

  • ObsessiveMathsFreak
  • · Replies 8 ·
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8

Graduate Proving Wedge Product Property for Alternating Tensors

  • ak416
  • · Replies 11 ·
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11

Graduate Does Pi Change in Curved Space Geometry?

  • Coloured_muffin
  • · Replies 2 ·
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2

Graduate Is Einstein Notation Used Consistently in Tensor Analysis on R³?

  • quasar987
  • · Replies 7 ·
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7

Graduate How Can I Visualize the Exterior Derivative 'd' in Differential Geometry?

  • r16
  • · Replies 89 ·
3
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89

Graduate Possible Generalization of Cross Product?

  • SeReNiTy
  • · Replies 7 ·
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7

Graduate Inner product Pythagoras theorem

  • motlking
  • · Replies 3 ·
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3

Graduate Principle Bundles: Right or Left Action?

  • pensano
  • · Replies 4 ·
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4

Graduate Spivak calculus on manifolds solutions? (someone asked this b4 and got ignored)

  • precondition
  • · Replies 6 ·
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6

Graduate Angle Between Planes: Is i1+cos(rotation)*i2 Correct?

  • tony873004
  • · Replies 6 ·
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6