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 Tangent vector as derivation question

  • orion
  • · Replies 9 ·
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9

Graduate Implicit Function Theorem Generalization

  • modnarandom
  • · Replies 2 ·
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2

Graduate Can contraction of a tensor be defined without using coordinates?

  • andrewkirk
  • · Replies 2 ·
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2

Graduate Learn Submanifold Definition in Differential Geometry

  • orion
  • · Replies 17 ·
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17

Graduate Get vector position projected on line

  • twoski
  • · Replies 1 ·
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1

Graduate Definition of tensors - abstract and concrete

  • hunt_mat
  • · Replies 5 ·
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5

Graduate How to prove the bilinearity of a given metric using tensorial product addition?

  • Simone Furcas
  • · Replies 4 ·
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4

Graduate What is the mistake in my coordinate transformation for Theorema Egregium?

  • Simone Furcas
  • · Replies 4 ·
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4

Graduate Projection of a point from one plane onto another

  • cptolemy
  • · Replies 7 ·
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7

Graduate Local parameterizations and coordinate charts

  • "Don't panic!"
  • · Replies 14 ·
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14

Graduate Equidistant points on the suface of a sphere

  • rootone
  • · Replies 16 ·
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16

Undergrad Excellent video series raises good question:

  • BiGyElLoWhAt
  • · Replies 6 ·
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6

Graduate Raising and Lowering Indices and metric tensors

  • Physicist97
  • · Replies 4 ·
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4

Undergrad What are the normalized vectors in polar coordinates?

  • Bruno Tolentino
  • · Replies 8 ·
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8

Graduate Differentiating maps between vector spaces

  • modnarandom
  • · Replies 5 ·
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5

Undergrad Hyperbolic space game: math help

  • googolplexking
  • · Replies 4 ·
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4

Graduate Displacement Operator: Exponential of Parameter & Vector?

  • dyn
  • · Replies 8 ·
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8

Undergrad Sphere in Cube: Can it be Defined?

  • Atlas3
  • · Replies 13 ·
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13

Graduate Coordinate charts and change of basis

  • "Don't panic!"
  • · Replies 17 ·
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17

Graduate Understanding the Gradient in Different Coordinate Systems

  • bronxman
  • · Replies 14 ·
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14

Graduate Calculating Area on Sphere: Unit Sphere & Rings

  • Vrbic
  • · Replies 4 ·
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4

Graduate Are There Special Properties of Geodesics in a Lie Group?

  • Andre' Quanta
  • · Replies 2 ·
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2

Undergrad Point movement on a surface of a sphere

  • Sobe118
  • · Replies 7 ·
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7

Graduate Could someone critique this? (Lie Group with the Lie Algebra)

  • bronxman
  • · Replies 14 ·
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14

Graduate Calculus on Manifolds: Lie Algebra, Lie Groups & Exterior Algebra

  • bronxman
  • · Replies 7 ·
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7

Graduate What are the key differences between a manifold and a submanifold?

  • bronxman
  • · Replies 9 ·
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9

Graduate Torus parametrization and inverse

  • Jess_l
  • · Replies 1 ·
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1

Graduate Differential map between tangent spaces

  • "Don't panic!"
  • · Replies 12 ·
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12

Graduate Proof of dimension of the tangent space

  • hideelo
  • · Replies 8 ·
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8

Graduate Principal normal and curvature of a helix

  • kkz23691
  • · Replies 6 ·
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6

Graduate Infinitesimal displacement in spherical coordinates

  • PWiz
  • · Replies 3 ·
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3

Graduate Understanding the Tensor Product of Two One-Forms in Differential Geometry

  • "Don't panic!"
  • · Replies 2 ·
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2

Graduate As accurately as possible draw a curve in the real space R2

  • starterYEAR
  • · Replies 2 ·
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2

High School What is the Measure of Angle BAC in This Circle Geometry Problem?

  • PsychonautQQ
  • · Replies 2 ·
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2

Graduate Surface joining two points in a family of concentric spheres

  • DivGradCurl
  • · Replies 9 ·
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9

Graduate The speed of a curve in different coordinate systems

  • kkz23691
  • · Replies 4 ·
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4

Graduate Why is a gradient not always a vector

  • Alain De Vos
  • · Replies 4 ·
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4

Graduate Problem with definition of tensor

  • ShayanJ
  • · Replies 10 ·
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10

Graduate Proof the shortest path on a sphere is the great circle.

  • trytodoit
  • · Replies 10 ·
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10

Graduate Projection stereographic and second fundamental form

  • Simone Furcas
  • · Replies 4 ·
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4

Undergrad Parametric equations of various shapes

  • Raghav Gupta
  • · Replies 3 ·
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3

Graduate Counting Degrees of Freedom in Tensor

  • "pi"mp
  • · Replies 13 ·
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13

Graduate Ricci tensor equals zero implies flat splace?

  • Abrahamsk8
  • · Replies 3 ·
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3

Graduate Curve extrapolation: polynomial or Bézier?

  • MisterH
  • · Replies 8 ·
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8

Undergrad How to convert a hyperbolic system to cartesian?

  • Bruno Tolentino
  • · Replies 5 ·
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5

Undergrad Equation of family of circles

  • AdityaDev
  • · Replies 3 ·
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3

Graduate Noethers theorem, physics and mathematics

  • JVM
  • · Replies 7 ·
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7

Graduate How to derive the formula for moment of inertia of polygon?

  • trytodoit
  • · Replies 2 ·
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2

Graduate A technical question that has to do with Hodge Star

  • PhyAmateur
  • · Replies 8 ·
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8

Graduate 'curve-in' condition in an equiangular spiral

  • Corse
  • · Replies 1 ·
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1

Graduate Minimal Surface between two different coaxial circules

  • RafaelPetros
  • · Replies 7 ·
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7

Graduate Integration of Ricci Scalar Over Surface

  • darida
  • · Replies 5 ·
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5

Graduate Parametrizing a Complex Curve on a Torus Surface

  • TESL@
  • · Replies 2 ·
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2

Graduate Rotation matrix about an arbitrary axis

  • Happiness
  • · Replies 2 ·
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2

Graduate Rotate a three-sphere so every point moves in R^4?

  • Spinnor
  • · Replies 4 ·
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4

Graduate Constructing S^3 from a S^2 and a bunch of S^1's?

  • Spinnor
  • · Replies 13 ·
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13

Graduate Why $H$ is a (1,2) tensor field?

  • CAF123
  • · Replies 3 ·
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3

Graduate Do not understand concept of Riemann geometry.

  • Enrico Fermi
  • · Replies 1 ·
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1

Graduate Hodge duality and differential forms

  • PhyAmateur
  • · Replies 4 ·
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4

Graduate Levi-Civita Symbol and indefinite metrics

  • Geometry_dude
  • · Replies 2 ·
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2

Graduate Equation (with polar coordinates) of circle on a sphere

  • mario991
  • · Replies 5 ·
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5

Graduate What is an inclusion map? (manifolds)

  • Fellowroot
  • · Replies 6 ·
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6

Undergrad How to Find the Area of a Truncated Ellipse?

  • AlexK864
  • · Replies 4 ·
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4

Graduate Confocal ellipse and hyperbola

  • Ananya0107
  • · Replies 6 ·
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6

Graduate How Does Gradient Impact Sphere Rolling Direction on a Surface?

  • uzman1243
  • · Replies 13 ·
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13

Graduate What is the interpretation of dx in calculus?

  • "Don't panic!"
  • · Replies 48 ·
2
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48

Graduate Set of points in S^3, way to show spaced equal or not?

  • Spinnor
  • · Replies 1 ·
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1

Graduate Pi and the curvature of the universe

  • Cato
  • · Replies 6 ·
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6

Graduate Curves and tangent vectors in a manifold setting

  • CAF123
  • · Replies 2 ·
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2

Graduate Integrating Forms on Manifolds: Understanding the Concept and Techniques

  • "Don't panic!"
  • · Replies 25 ·
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25

Graduate Tangent vectors as directional derivatives

  • "Don't panic!"
  • · Replies 36 ·
2
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36

Graduate Can one "chop" up S^3 into little cubes?

  • Spinnor
  • · Replies 1 ·
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1

Graduate Understanding Manifolds: Questions & Answers

  • Fellowroot
  • · Replies 4 ·
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4

Graduate Working out a point / segment on a sphere

  • rede96
  • · Replies 3 ·
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3

Graduate Intuition and existence for convex neighbourhoods

  • center o bass
  • · Replies 5 ·
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5

Find Length of Arc EF in Triangle ABC

  • Albert1
  • · Replies 2 ·
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2

Graduate Why are vectors defined in terms of curves on manifolds

  • "Don't panic!"
  • · Replies 14 ·
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14

Graduate What is the parity inversion of antisymmetric tensor

  • genxium
  • · Replies 2 ·
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2

Graduate Calculating Equations of Ellipses Within a Cone

  • cpman
  • · Replies 3 ·
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3

Graduate A suggested operational definition of tensors

  • Will Flannery
  • · Replies 2 ·
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2

Graduate Koszul Connexion: Explained Simply

  • Calabi
  • · Replies 8 ·
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8

Graduate Attempting to understand diffeomorphisms

  • "Don't panic!"
  • · Replies 16 ·
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16

Graduate Is this a valid parametrization of the torus?

  • hideelo
  • · Replies 3 ·
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3

Graduate What Does Equation 5.7 in Introducing Einstein's Relativity Really Mean?

  • Corbeau
  • · Replies 8 ·
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8

Graduate Question about geometric algebra -- Can any one help?

  • Summetros
  • · Replies 1 ·
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1

Graduate Confusion About Notation with Tensors

  • B3NR4Y
  • · Replies 5 ·
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5

Any value to Spivak's Differential Geometry set?

  • toozie21
  • · Replies 6 ·
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6

Graduate Diffeomorphisms and active transformations

  • "Don't panic!"
  • · Replies 4 ·
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4

Graduate A question on defining vectors as equivalence classes

  • "Don't panic!"
  • · Replies 14 ·
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14

Graduate How does regularity of curves prevent "cusps"?

  • center o bass
  • · Replies 3 ·
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3

Graduate Show that this vector is timelike?

  • Dixanadu
  • · Replies 9 ·
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9

PDE or differentiable manifolds?

  • mathmari
  • · Replies 3 ·
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3

Graduate Difference between "intrinsic"and "parametric" curvature

  • hideelo
  • · Replies 2 ·
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2

Search for Senior Undergraduate Text on Lie Theory and Groups

  • Math Amateur
  • · Replies 6 ·
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6

Graduate Where do I start learning differential geometry?

  • PWiz
  • · Replies 1 ·
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1

Graduate Lie Dragging and Lie Derivatives

  • Zag
  • · Replies 9 ·
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9

Graduate Questions about tangent spaces & the tangent bundle

  • "Don't panic!"
  • · Replies 11 ·
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11

Graduate Understanding the notion of a tangent bundle

  • "Don't panic!"
  • · Replies 17 ·
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17

Graduate Tensor Fields - Tensor Product of Two Gradient Operators

  • barnflakes
  • · Replies 3 ·
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3

Graduate Surface area of a region of a torus

  • O2F
  • · Replies 5 ·
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5