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 Geodesics in Modified Euclidean Spaces: Is There a General Statement?

  • ledol83
  • · Replies 6 ·
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6

Graduate Connections in differential geometry

  • Coin
  • · Replies 13 ·
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13

Undergrad Where Can I Find Tensor Learning Resources with Solved Examples and Exercises?

  • freak_rj
  • · Replies 1 ·
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1

Graduate Some elementary geometry questions

  • haushofer
  • · Replies 14 ·
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14

Graduate What Does the Matrix A Represent in Manifold Gradient Calculations?

  • Asuralm
  • · Replies 1 ·
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1

Graduate What is the connection between discrete torus geometry and lines on an NxN grid?

  • Galileo
  • · Replies 6 ·
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6

Graduate Differential forms and divergence

  • Damidami
  • · Replies 9 ·
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9

Graduate How Do Nearby Geodesics Deviate in Curved Spaces?

  • ledol83
  • · Replies 1 ·
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1

Graduate Is (S^n) X R Parallelizable for All n?

  • amd939
  • · Replies 3 ·
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3

Undergrad Convert the coordiates of one vector between 2 Cartesian system

  • bigworld005
  • · Replies 3 ·
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3

Graduate Why does one form need to be used over the other?

  • nrqed
  • · Replies 65 ·
3
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65

Graduate Isometric Immersion: Finding Geodesic Curves

  • brown042
  • · Replies 1 ·
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1

Graduate Christoffel symbols from definition or Lagrangian

  • noospace
  • · Replies 6 ·
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6

Graduate How Do Induced Maps Affect Higher Rank Tensors?

  • quasar_4
  • · Replies 1 ·
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1

Graduate Tensor Analysis Basics for Non-Experts

  • quasar_4
  • · Replies 13 ·
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13

Undergrad Arc Length of an Ellipse: Formula & Calculation

  • natski
  • · Replies 6 ·
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6

Graduate Is the Submersion Property Preserved in Maps Between R and S^1?

  • quasar987
  • · Replies 3 ·
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3

Graduate Why are tangent vectors like this?

  • jostpuur
  • · Replies 4 ·
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4

Graduate Symmetrizing and skew symmetrizing tensors

  • quasar_4
  • · Replies 1 ·
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1

Graduate Is the Boundary of an n-Dimensional Space Always n-1 Dimensional?

  • princeton118
  • · Replies 6 ·
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6

Graduate Identities for covariant derivative

  • CompuChip
  • · Replies 4 ·
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4

Graduate To distinguish if a critical point is a saddle point or not,. .

  • alexio
  • · Replies 1 ·
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1

Graduate Proving Existence of Vector Field X for 1-Form w on Smooth Manifold M

  • daishin
  • · Replies 6 ·
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6

Graduate Proof of Proposition 2 in Ch.7 Spivak Vol.2: n-Dimensional Distribution?

  • joe2317
  • · Replies 1 ·
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1

Graduate Differential Forms on Smooth Manifolds

  • daishin
  • · Replies 3 ·
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3

Graduate Can this vector equation be proven?

  • R3DH34RT
  • · Replies 7 ·
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7

Undergrad How Do You Reverse a Vector Transformation?

  • R3DH34RT
  • · Replies 4 ·
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4

Graduate Comprehensive intro to diff geometry by Spivak Vol2.

  • brown042
  • · Replies 13 ·
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13

Undergrad Create bezier curve from 2 conected curve

  • temp
  • · Replies 2 ·
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2

Graduate What is the purpose of contraction in tensor algebra?

  • joe2317
  • · Replies 4 ·
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4

Graduate Tensor Newbie trying to find Kolecki's rhythm

  • jbowers9
  • · Replies 11 ·
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11

Graduate Holonomy, SO(6), SU(3) and SU(4)

  • AlphaNumeric2
  • · Replies 2 ·
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2

Graduate The Cramer-Euler-McLaurin Paradox

  • Chris Hillman
  • · Replies 12 ·
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12

Graduate Evaluate Ai = (Epsilon)ijk bj bk

  • R3DH34RT
  • · Replies 18 ·
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18

Graduate Solved problems on manifolds: A resource for physics students

  • ala
  • · Replies 15 ·
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15

Graduate Simple questions about weyl rescaling/Conformal transfo

  • nrqed
  • · Replies 7 ·
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7

Graduate Exact definition of differential forms

  • cogito²
  • · Replies 9 ·
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9

Undergrad Describing Curvature of a Non-Uniform Curve Using Second Derivative Average?

  • ice109
  • · Replies 7 ·
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7

Graduate Help with Lagrangian to Eulerian transformation

  • jon8105
  • · Replies 1 ·
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1

Graduate Taking a course in calculus on manifolds.

  • MathematicalPhysicist
  • · Replies 9 ·
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9

Graduate Symmetric Matrices as Submfld. of M_n. Prelim

  • WWGD
  • · Replies 10 ·
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10

Graduate Help with universal theorem of coefficients for homology

  • Coolphreak
  • · Replies 1 ·
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1

Graduate What is the significance of \hat{\theta} in polar vector coordinates?

  • ice109
  • · Replies 4 ·
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4

Graduate Proving Equivalence of Lie Bracket Definitions for Lie Groups

  • Fredrik
  • · Replies 4 ·
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4

Graduate There is one point I don't understand about G-torsor.

  • kakarukeys
  • · Replies 4 ·
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4

Graduate One-Parameter Groups:John Lee's Vector Field Analysis

  • WWGD
  • · Replies 3 ·
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3

Graduate Poisson's Identity: Solving ((φλ)χ)+((λχ)φ)+((χφ)λ)=0

  • aggarwal
  • · Replies 1 ·
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1

Graduate Thurston Geometries: Get the Facts on Left-Invariant Metrics

  • Reverie
  • · Replies 3 ·
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3

Graduate Is a Function from R^n to R^m Considered a 0-Form on R^n?

  • quasar987
  • · Replies 9 ·
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9

Undergrad Sketch of curves defined by parameters

  • smoothman
  • · Replies 3 ·
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3

Graduate What Is First-Countability in a Metric Space: Missed Point Explained

  • matness
  • · Replies 11 ·
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11

Undergrad Deriving the Surface Area of Sphere

  • ron_jay
  • · Replies 7 ·
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7

Graduate Tensor Conventions for Contravariant and Covariant Notation

  • quasar987
  • · Replies 1 ·
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1

Graduate Smooth Charts on immersion image.

  • WWGD
  • · Replies 0 ·
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0

Graduate Continuous Function f: A x B to C

  • kakarukeys
  • · Replies 8 ·
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8

Graduate The Lie Derivative: Physical Significance & Tensor Analysis

  • captain
  • · Replies 2 ·
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2

Graduate Understanding Scalars in Mathematical Physics: Insights and Clarifications

  • pmb_phy
  • · Replies 25 ·
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25

Graduate Sufficient Condition for Adjoint Representation Kernel to be Lie Group Center

  • kakarukeys
  • · Replies 1 ·
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1

Graduate Why is Schouten's book on tensor analysis not recommended for physicists?

  • uiulic
  • · Replies 1 ·
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1

Graduate Intro to tensor material - If you have time please

  • pmb_phy
  • · Replies 15 ·
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15

Undergrad Why is Time Considered a Scalar in Mathematics and Physics?

  • uiulic
  • · Replies 3 ·
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3

Graduate How can the isomorphism of pullback bundles by homotopic maps be proven?

  • kakarukeys
  • · Replies 6 ·
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6

Graduate Tangent spaces and derivations

  • StatusX
  • · Replies 14 ·
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14

Graduate Angle preserving transformations

  • bigli
  • · Replies 1 ·
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1

Graduate Learn About Grassmann Manifolds: Intro, Charts, Atlas

  • bigli
  • · Replies 5 ·
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5

Graduate How to relate a one form to a vector.

  • matheinste
  • · Replies 29 ·
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29

Graduate A simple derivation involving the Hodge dual

  • nrqed
  • · Replies 4 ·
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4

Graduate Can You Perform Vector Calculations in Fractal Dimensions?

  • Niv
  • · Replies 3 ·
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3

Graduate Discovering the Functions of $\Bbb{R}^{2}\times _{\phi }\Bbb{R}$ in 3D Lie Groups

  • Reverie
  • · Replies 3 ·
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3

Graduate Evaluating Symmetric/Antisymmetric Tensors Rank 5 Dimension 999

  • Rahat
  • · Replies 1 ·
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1

Graduate Elementary Differential Geometry Questions

  • Saketh
  • · Replies 11 ·
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11

Graduate How to Find the Inverse of a 4th Order Tensor in the Isotropic Case

  • titous
  • · Replies 6 ·
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6

Graduate How many coordinate charts does it take to cover a surface?

  • DeadWolfe
  • · Replies 12 ·
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12

Undergrad Proving the theorem (Appolonius) for the triangle ABC where..

  • thagamizer
  • · Replies 2 ·
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2

Graduate How to Prove contracted Bianchi Identity

  • jojoo
  • · Replies 5 ·
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5

Graduate Limitations of Tensor Analysis in Physical Laws

  • uiulic
  • · Replies 24 ·
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24

What Are Tensors and Why Should You Care?

  • uiulic
  • · Replies 12 ·
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12

Graduate What is the formula for defining curvature on three-dimensional surfaces?

  • KingBongo
  • · Replies 10 ·
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10

Graduate How Does the Selberg Trace Formula Connect Eigenvalues and Manifold Properties?

  • tpm
  • · Replies 1 ·
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1

Graduate Expressing the Minkowski Field Tensor for Circular Currents

  • Norman Albers
  • · Replies 4 ·
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4

Graduate Slow Roll Parameters: Deriving and Computing

  • AlphaNumeric
  • · Replies 1 ·
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1

Curve with ever increasing radius

  • bobbobwhite
  • · Replies 5 ·
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5

Graduate Can a stress tensor be curled in physics?

  • touqra
  • · Replies 7 ·
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7

Graduate How Is the Weyl Tensor Derived?

  • SeReNiTy
  • · Replies 18 ·
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18

Graduate Higher Order Tensor: Learn Calculation Rules & Get Info

  • blue angel
  • · Replies 2 ·
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2

Graduate What are the expressions for CURL in spherical coordinates?

  • Norman Albers
  • · Replies 15 ·
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15

Graduate Building Invariants from Vector, Levi-Civita Symbol

  • tannin
  • · Replies 6 ·
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6

Graduate Understanding the Contravariant Derivative: A Tangential and Normal Perspective

  • bchui
  • · Replies 3 ·
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3

Graduate Bilinear forms and wedge products

  • homology
  • · Replies 4 ·
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4

Graduate What is the Spacetime Metric and its Describing Equations in Layman's Terms?

  • delta001
  • · Replies 12 ·
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12

Graduate What is the relationship between k-forms and l-forms on an m-manifold?

  • blendecho
  • · Replies 1 ·
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1

Graduate Solving Ricci Tensor Problem: Schwarzschild Metric

  • Mentz114
  • · Replies 16 ·
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16

Graduate Help with paper on gradient descent evolution of surfaces

  • danrop
  • · Replies 2 ·
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2

Graduate Exact sequence & meaning of a corollary?

  • Firefly!
  • · Replies 6 ·
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6

Undergrad Math Newb Wants to know what a Tensor is

  • StonedPanda
  • · Replies 90 ·
4
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90

Undergrad Rotating 2D coordinate geometry/conic sections into 3D - how?

  • chaoseverlasting
  • · Replies 7 ·
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7

Graduate Is a Second Order Symmetric Tensor Always Represented by a Symmetric Matrix?

  • BobbyFluffyPric
  • · Replies 10 ·
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10

Undergrad What Are Partitions of Unity in Mathematics?

  • Terilien
  • · Replies 1 ·
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1

High School Poincare Conjecture Explained: Layman's Terms

  • Ragnar
  • · Replies 7 ·
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7

Graduate How Do Changes in Curvilinear Coordinates Affect Unit Vectors?

  • Swapnil
  • · Replies 9 ·
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9