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 Covariant derivative of a commutator (deriving Bianchi identity)

  • center o bass
  • · Replies 3 ·
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3

Graduate Problem with Einstein notation and Levi-Civita symbol

  • mnb96
  • · Replies 8 ·
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8

High School When to use alpha vs theta for angles

  • PhysEd
  • · Replies 6 ·
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6

Graduate What are some applications of Lie derivative in physics?

  • christianpoved
  • · Replies 7 ·
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7

Graduate Is a (hyper)sphere a (hyper)plane in spherical coordinates?

  • bers
  • · Replies 1 ·
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1

Graduate How to Map Points Between the Poincaré Disk and the Cartesian Plane?

  • mnb96
  • · Replies 9 ·
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9

How Do Frenet Equations Relate Torsion to Time Derivatives of Position?

  • Dustinsfl
  • · Replies 2 ·
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2

Graduate Can l'Hopital's Rule Be Generalized for Differentiable Maps Between Manifolds?

  • Mandelbroth
  • · Replies 2 ·
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2

Curvature and torsion on a helix

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Arc length of a regular parametrized curve

  • tuggler
  • · Replies 2 ·
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2

Fernet-Serrat equations and vector calculus

  • Dustinsfl
  • · Replies 2 ·
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2

Graduate Calculating area with the metric

  • Benjam:n
  • · Replies 1 ·
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1

Undergrad How to Begin Solving a Basic Open B-Spline Curve with Given Control Points?

  • vee6
  • · Replies 11 ·
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11

Undergrad Unit vectors in polar co ordinates

  • manimaran1605
  • · Replies 1 ·
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1

Graduate Intuition behind two manifolds being the same.

  • center o bass
  • · Replies 22 ·
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22

Find the altitude of the triangle with minimum area

  • MarkFL
  • · Replies 2 ·
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2

Graduate Integral Notation: Abuse or Necessity?

  • Mandelbroth
  • · Replies 3 ·
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3

Graduate Showing that the Lie derivative of a function is the directional deriv

  • center o bass
  • · Replies 4 ·
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4

Graduate Transformation relations tensors

  • roldy
  • · Replies 1 ·
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1

Undergrad Links for these concepts please

  • manimaran1605
  • · Replies 7 ·
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7

Graduate Line of maximum for a 2D 'surface'

  • Karthiksrao
  • · Replies 1 ·
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1

Graduate Inverse Jacobi Matrix in Spherical Coordinates

  • Coelum
  • · Replies 6 ·
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6

Graduate What is the value of δ^{λ}_{μ} in 4 dimensions?

  • Dreak
  • · Replies 2 ·
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2

Surface of Revolution: Find Equation & Identify Surface

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate What is the Hodge dual and how does it work?

  • AlbertEi
  • · Replies 11 ·
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11

Let L1 be the line through P and Q

  • karush
  • · Replies 3 ·
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3

Classification/terminology for shape of a curve

  • ATroelstein
  • · Replies 3 ·
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3

Find the Largest Sphere That Will Fit Inside a Pyramid

  • anemone
  • · Replies 2 ·
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2

Graduate Why can't elliptical space exist?

  • acesuv
  • · Replies 8 ·
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8

Graduate Are Isometric Metric Spaces Identical?

  • Whovian
  • · Replies 1 ·
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1

Graduate Calculating the Pullback of a 1-Form on S1 by a Differentiable Map

  • WWGD
  • · Replies 1 ·
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1

How to Calculate the Radius of a Circle Tangent to Two Lines?

  • ginger
  • · Replies 4 ·
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4

Graduate What is the Issue with Tensor Contraction Notation?

  • littleHilbert
  • · Replies 10 ·
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10

Graduate First Fundamental Form from tangent vectors

  • larry_b
  • · Replies 1 ·
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1

Find Tangent Lines to Polar Graph: r=2-3sin(θ)

  • MarkFL
  • · Replies 1 ·
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1

Graduate Tensor summation and components.

  • peripatein
  • · Replies 11 ·
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11

Graduate Obtaining spherical coordinates by rotations

  • Niles
  • · Replies 3 ·
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3

Graduate Recursive 3D Tiling of Rhombic Dodecahedra

  • Ventrella
  • · Replies 1 ·
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1

Graduate Little Spivak-Winding Number: Integrating Forms over Chains

  • sammycaps
  • · Replies 16 ·
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16

Graduate Plausibility of a Discrete Point Manifold

  • Mandelbroth
  • · Replies 5 ·
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5

Graduate S^2 × S^2...×S^2×S^2 is a Direct Product of S^2 - Hypertorus

  • LagrangeEuler
  • · Replies 1 ·
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1

Graduate When can we extend the minimal geodesics indefinitely?

  • Dragonfall
  • · Replies 16 ·
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16

Proving a Statement about a Regular Curve: R of Area k

  • Fernando Revilla
  • · Replies 1 ·
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1

Graduate Einstein Notation for Stored Energy Function

  • singularme
  • · Replies 1 ·
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1

Graduate Riemannian Manifolds: Extending Geodesics Indefinitely

  • Dragonfall
  • · Replies 1 ·
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1

Graduate How is Stone's Theorem Related to Lie Algebras and Unitary Groups?

  • mma
  • · Replies 5 ·
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5

Undergrad How does Lie group help to solve ode's?

  • ayan849
  • · Replies 20 ·
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20

Graduate Are second derivative symmetric in a Riemannian manifold?

  • fairy._.queen
  • · Replies 4 ·
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4

Graduate Why is the trace of jacobian=the divergence?

  • marellasunny
  • · Replies 4 ·
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4

Graduate Parameters of helix approximated by parts of torus

  • lewhoo
  • · Replies 1 ·
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1

Graduate What is the issue with tensor terminology and variable slot order?

  • Fredrik
  • · Replies 11 ·
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11

Undergrad Point of Contact Between Arc and Circle

  • mjgarrin
  • · Replies 1 ·
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1

Graduate Spivak's Differential Geometry I

  • sammycaps
  • · Replies 3 ·
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3

Graduate What exactly is differential geometry?

  • pierce15
  • · Replies 5 ·
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5

Graduate Is There a Difference Between Covariant and Contravariant Tensor Notations?

  • Markus Hanke
  • · Replies 3 ·
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3

Undergrad Converting from cartesian to spherical boundaries

  • dan38
  • · Replies 1 ·
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1

Graduate General rule product matrices?

  • Yoran91
  • · Replies 1 ·
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1

High School Solving an equation: finding the arc length

  • rockwusho
  • · Replies 7 ·
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7

Graduate Conditions for using Stokes' Theorem

  • Mandelbroth
  • · Replies 7 ·
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7

Graduate General Doubts on Ehresmann Connections

  • WWGD
  • · Replies 3 ·
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3

Graduate Metric Tensor on a Mobius Strip?

  • Mandelbroth
  • · Replies 3 ·
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3

Graduate Visualising the exterior derivative ?

  • Markus Hanke
  • · Replies 11 ·
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11

Graduate Fiber bundles and the fiber for Electromagnetism.

  • Spinnor
  • · Replies 7 ·
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7

Graduate HELP with Killing Vectors in AdS

  • llorgos
  • · Replies 4 ·
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4

Graduate Metric on torus induced by identification of points on plane

  • Illuminatum
  • · Replies 6 ·
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6

Undergrad Basic understanding of differential geometry

  • shounakbhatta
  • · Replies 7 ·
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7

Graduate Mapping 4D torus onto 4-sphere non-trivially

  • nonequilibrium
  • · Replies 8 ·
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8

Graduate Calculation: Formula for Laplacian/tr(Hess)

  • Sajet
  • · Replies 2 ·
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2

Graduate Symmetry of connection coefficients? (simple question)

  • pellman
  • · Replies 2 ·
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2

Graduate Transformation matrixes and tensors

  • joda80
  • · Replies 11 ·
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11

Graduate Analysis of 4D Space-Time Distribution

  • alejandrito29
  • · Replies 1 ·
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1

Graduate Trying to understand derivatives in terms of differential forms

  • Mandelbroth
  • · Replies 7 ·
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7

Graduate Does an algebraic function always ramify at a multiple root?

  • jackmell
  • · Replies 7 ·
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7

Graduate Question on generalized inner product in tensor analysis

  • mnb96
  • · Replies 4 ·
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4

Graduate Inner product in curvilinear coordinates

  • mnb96
  • · Replies 15 ·
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15

Graduate What is a Knot Vector and How Do You Find Its Value?

  • mymachine
  • · Replies 3 ·
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3

Graduate Is the curl of a field a vector or a vector density?

  • joda80
  • · Replies 2 ·
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2

Undergrad Cartesian to Polar: Angle Theta Interval Defined

  • jamesb1
  • · Replies 1 ·
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1

Graduate Surfaces without an explicit representation.

  • jamesb1
  • · Replies 9 ·
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9

Graduate Covariant Versus Contravariant Vectors

  • pbhact
  • · Replies 21 ·
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21

Graduate What is the concept of a line in higher than 3D space?

  • ftr
  • · Replies 9 ·
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9

Graduate Euler characteristic as a total derivative

  • electroweak
  • · Replies 2 ·
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2

Graduate A general theory for reducing the number of variables?

  • Stephen Tashi
  • · Replies 2 ·
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2

Graduate How Can I Fix My Indicial Notation Practice?

  • muzialis
  • · Replies 1 ·
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1

Graduate Principle curvature: min and max curvature are always perpendicular?

  • Relative0
  • · Replies 3 ·
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3

Graduate How should I approach this (coordinate transformation) problem?

  • Swulf
  • · Replies 3 ·
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3

Graduate What Does d/dt g(t) and d/dt D_X Y Mean in Riemannian Manifold Calculations?

  • Sajet
  • · Replies 6 ·
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6

Undergrad Dr/dt = (dr/du)(du/dt) + (dr/dv)(dv/dt)

  • jamesb1
  • · Replies 3 ·
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3

Graduate Jacobi identity in local coordinates?

  • quasar987
  • · Replies 1 ·
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1

Most efficient way to identify a circle

  • Rashad9607
  • · Replies 6 ·
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6

Graduate Parametrizations of the 3-sphere

  • jk22
  • · Replies 3 ·
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3

Graduate Can Diffeomorphisms be Represented by Matrices and Used in Image Analysis?

  • garrus
  • · Replies 4 ·
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4

Graduate Help Me Understand Differential Forms on Riemannian Manifolds

  • Kontilera
  • · Replies 8 ·
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8

Graduate True Algebraic Nature of Tensors

  • Rising Eagle
  • · Replies 9 ·
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9

Graduate 2-dimensional differentiable surfaces

  • Dragonfall
  • · Replies 3 ·
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3

Graduate Topological property of the Cantor set

  • hedipaldi
  • · Replies 4 ·
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4

Graduate Connection forms on manifolds in Euclidean space

  • lavinia
  • · Replies 0 ·
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0

Undergrad Fitting the 'tightest' rectangle to a set of three dimensional points

  • Cbas
  • · Replies 3 ·
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3

Joko123's question at Yahoo Answers (Sketching a cone)

  • Fernando Revilla
  • · Replies 1 ·
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1

High School How can a curve be one dimensional?

  • rollcast
  • · Replies 26 ·
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26