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 Surface area of a region of a torus

  • O2F
  • · Replies 5 ·
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5

Graduate Geometric definition of the fourth dimension and tessaracts

  • shawnr
  • · Replies 7 ·
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7

Graduate Bundle and differential manifold

  • Calabi
  • · Replies 6 ·
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6

Graduate What is a fiber bundle and how is it related to smooth manifolds?

  • Fredrik
  • · Replies 16 ·
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16

Undergrad Evaluating $$ (a \wedge b)(c\wedge d)(e \wedge f)(g \wedge h) $$

  • PhyAmateur
  • · Replies 4 ·
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4

HIGHLY Rigorous Treatment of the Trigonometric Functions

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Are Jacobi fields defined at intersection points?

  • Matterwave
  • · Replies 14 ·
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14

Graduate Constructing an Atlas for ##S^2## with Spherical Coordinates

  • Geometry_dude
  • · Replies 7 ·
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7

Graduate Mapping of the standard k-simplex in R^n to X

  • cpsinkule
  • · Replies 1 ·
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1

Graduate Boundary operator formula for simplices in de Rham theory

  • cpsinkule
  • · Replies 13 ·
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13

Graduate Translation from vector calc. notation to index notation

  • JonnyMaddox
  • · Replies 8 ·
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8

Graduate Rope tangent angle over pully given position of offset load

  • Wayland Bugg
  • · Replies 9 ·
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9

Graduate Calculate moment of inertia of a "L" angle bent in a parabola

  • Shaheen Uqab
  • · Replies 13 ·
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13

Graduate Hodge duality and some properties

  • PhyAmateur
  • · Replies 6 ·
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6

Undergrad Foundations of Geometry Reading Suggestions?

  • Charles Stark
  • · Replies 3 ·
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3

Graduate Metrics and Group Structure Reduction

  • Oxymoron
  • · Replies 5 ·
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5

Graduate Boundary of a chain, Stokes' theorem.

  • Kim.S.H
  • · Replies 2 ·
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2

Graduate Which Fields Are Naturally Manifolds Beyond ##\mathbb{R}## and ##\mathbb{C}##?

  • WWGD
  • · Replies 8 ·
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8

Graduate Vectors in Tangent Space to a Manifold Independent of Coordinate Chart

  • "Don't panic!"
  • · Replies 18 ·
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18

Graduate Differentiability of a function on a manifold

  • "Don't panic!"
  • · Replies 3 ·
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3

Graduate Covariant equation intuition confusing me

  • NotASmurf
  • · Replies 13 ·
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13

Graduate Equation for a tilted parabola in 3D?

  • 2sin54
  • · Replies 2 ·
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2

What to expect from a differential equations course?

  • ineedhelpnow
  • · Replies 2 ·
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2

Graduate ± sqrt(b^2 - a^2) = ± b ± ai ?

  • Philip
  • · Replies 6 ·
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6

Graduate Curve Matching Techniques for Rotated Curves in Geometric Analysis

  • klau
  • · Replies 1 ·
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1

Graduate Vectors as a differential op and covectors as differenential

  • binbagsss
  • · Replies 2 ·
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2

Undergrad 3D geometry: parametric equation and tangents

  • AdityaDev
  • · Replies 1 ·
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1

Graduate Closed-space sphere "displacement"?

  • bahamagreen
  • · Replies 1 ·
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1

Graduate Legality and Generality of a Simplifying Method

  • ELB27
  • · Replies 2 ·
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2

Undergrad Proof of Cyclic Graph Edges = Vertices Formula

  • Charles Stark
  • · Replies 3 ·
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3

Graduate Demonstrating Tangent Space Independence in Manifolds

  • Calabi
  • · Replies 17 ·
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17

Graduate Conformal mapping from polygon with circle segments

  • Kurret
  • · Replies 1 ·
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1

Proving P∩Q=R∩S for Curves $P,Q,R,S$

  • anemone
  • · Replies 2 ·
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2

Graduate Can Pappus' Theorem Explain the Gaps on a Torus?

  • autodidude
  • · Replies 1 ·
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1

Graduate More on Universal Cover of a Surface with Boundary

  • WWGD
  • · Replies 1 ·
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1

Graduate Finding ellipse semiaxes and circle center tangent to an ellipse with given eccentricity

  • quantumdude
  • · Replies 6 ·
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6

Graduate Surface Area Vector in Exterior Algebra 3D

  • mikeeey
  • · Replies 7 ·
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7

Find the equation of parabola with vertex (2, 1) and focus (1, -1)

  • sagarsoni7
  • · Replies 3 ·
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3

Graduate What is the difference between covariant and contravariant tensors?

  • putongren
  • · Replies 2 ·
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2

Graduate What are the topological properties of the FLRW model?

  • kostas230
  • · Replies 4 ·
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4

Graduate If the Product Manifold MxN is orientable, so are M,N.

  • WWGD
  • · Replies 4 ·
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4

Graduate Classifications of basis vectors

  • mikeeey
  • · Replies 7 ·
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7

Graduate General method of parameterization

  • DivergentSpectrum
  • · Replies 3 ·
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3

Graduate Proving torsion and curvature forms with the canonical solder 1-form

  • mikeeey
  • · Replies 12 ·
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12

Graduate What is Tensor Calculus and How is it Related to Differential Geometry?

  • aditya ver.2.0
  • · Replies 2 ·
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2

Graduate Wrapping a 3D space wihtin a 4D space

  • Sebastien77
  • · Replies 4 ·
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4

Graduate Adjacency Matrix to Coordinate Transformations

  • lightfire
  • · Replies 4 ·
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4

Graduate Restricting Base of Bundle. Which Properties are Preserved?

  • WWGD
  • · Replies 1 ·
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1

High School Why is the Möbius strip considered closed?

  • ozlem
  • · Replies 1 ·
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1

Calculate the order of the point

  • evinda
  • · Replies 7 ·
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7

Graduate Hyperbolic Manifold With Geodesic Boundary?

  • WWGD
  • · Replies 5 ·
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5

Undergrad How to find normal vector to a square given its center and side length

  • hoang anh tuan
  • · Replies 6 ·
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6

Graduate Can't comb hair on a 2-sphere. On a Calabi Yau manifold?

  • Spinnor
  • · Replies 12 ·
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12

Graduate What can a complex manifold do for me that real manifolds can't.

  • Spinnor
  • · Replies 3 ·
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3

Graduate Do Coordinate Charts Alone Identify a Unit Circle?

  • dyn
  • · Replies 3 ·
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3

Graduate "Calabi-Yau Manifold for Dummies", short, at universe-review.ca"

  • Spinnor
  • · Replies 1 ·
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1

Graduate Atlas of torus and sphere. Atlas of Calabi–Yau manifold.

  • Spinnor
  • · Replies 3 ·
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3

Graduate Parallel transport on a cardioid

  • JonnyMaddox
  • · Replies 2 ·
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2

Graduate One-forms in differentiable manifolds and differentials in calculus

  • victorvmotti
  • · Replies 12 ·
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12

Graduate Surfaces of constant gradient-magnitude

  • JanEnClaesen
  • · Replies 1 ·
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1

Graduate Total derivative in action of the field theory

  • victorvmotti
  • · Replies 1 ·
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1

Graduate Radius of Triaxial / Scalene Ellipsoid

  • AwooOOoo
  • · Replies 1 ·
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1

Graduate Physics interpretation of integrals of differential forms

  • davi2686
  • · Replies 4 ·
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4

Undergrad What's the difference between tensors and vectors?

  • johann1301
  • · Replies 2 ·
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2

Graduate Why are affine connections called affine?

  • Geometry_dude
  • · Replies 1 ·
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1

Graduate Can \( d \omega = 0 \) Be Concluded from \( \int_{\partial S} \omega = 0 \)?

  • davi2686
  • · Replies 6 ·
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6

Graduate Loxodrome - found a mistake on Wolfram MathWorld site?

  • kkz23691
  • · Replies 11 ·
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11

Graduate The Grassmanian manifold's topology

  • camilus
  • · Replies 6 ·
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6

Graduate How Can I Obtain the 2-Form and P-Form Associated with a Vector Field?

  • davi2686
  • · Replies 6 ·
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6

Graduate Still wondering exp(so(N)) and SO(N)

  • jostpuur
  • · Replies 5 ·
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5

Graduate Can the Thickness of a 3D Spiral Curve be Defined Parametrically?

  • sukharef
  • · Replies 2 ·
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2

Graduate Why is loxodrome parametrization defined with tan⁻¹(at)?

  • kkz23691
  • · Replies 2 ·
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2

Graduate Spherical Coordinates Confusion: Which Set is Correct?

  • kkz23691
  • · Replies 4 ·
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4

Graduate Rectifying Curve: John Oprea's Differential Geometry Book

  • thoughtgaze
  • · Replies 1 ·
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1

Graduate Deriving spherical unit vectors in terms of cartesian unit vectors

  • chipotleaway
  • · Replies 2 ·
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2

Undergrad Identifying local maximum, local minimum and saddle point.

  • BondKing
  • · Replies 3 ·
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3

Graduate Formal Computations of Euler Classes

  • WWGD
  • · Replies 19 ·
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19

Graduate How to draw a 2D space in 3D Euclidean space by metric tensor

  • arpon
  • · Replies 1 ·
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1

Graduate How to prove Any curve in space can be written as for a parameter

  • persyan
  • · Replies 11 ·
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11

Graduate Mapping 3D point to cone surface using perpendicular line

  • mamort
  • · Replies 2 ·
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2

Graduate Multiplicity free fibers in maps between vector bundles

  • camilus
  • · Replies 1 ·
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1

Graduate Can Curvature Be Integrated Over Space in General Relativity?

  • friend
  • · Replies 5 ·
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5

Graduate Puzzled with the loxodrome ( spherical spiral ) equation

  • kkz23691
  • · Replies 7 ·
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7

Graduate Riemannian Geometry exponential map and distance

  • ireallymetal
  • · Replies 4 ·
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4

Undergrad Directional derivatives and the gradient vector

  • BondKing
  • · Replies 6 ·
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6

Graduate What is the Geometric Interpretation of Principal Bundles with Lie Group Fibres?

  • JonnyMaddox
  • · Replies 8 ·
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8

High School Understanding Transitional Lines to Parallel and Non-Parallel Lines

  • lightbender
  • · Replies 2 ·
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2

Graduate How to define covariant basis in curved space 'intrinsicly'?

  • arpon
  • · Replies 2 ·
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2

Graduate Are Euler-Lagrange Equations Applicable to All Differential Manifolds?

  • Incand
  • · Replies 2 ·
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2

Undergrad Determine center point of offset circle

  • examorph
  • · Replies 5 ·
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5

Graduate Understanding Euler Classes in Smooth Manifolds

  • lavinia
  • · Replies 4 ·
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4

Graduate Is Every Diff. Form on a Submanifold the Restriction of a Form in R^n?

  • WWGD
  • · Replies 7 ·
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7

Calculating Genus of a Curve Using Falting's Theorem

  • bitsmath
  • · Replies 4 ·
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4

Undergrad Changing the subject of an equation involving summation

  • resurgance2001
  • · Replies 9 ·
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9

Graduate Why is the infinitesimal parameter constant in Killing's equation?

  • synoe
  • · Replies 2 ·
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2

Graduate Elliptic geometry in 3 dimensions

  • TrickyDicky
  • · Replies 1 ·
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1

Graduate Stuggling with the abstraction of manifolds

  • dyn
  • · Replies 12 ·
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12

Graduate Connection on a principal bundle Intuition

  • center o bass
  • · Replies 11 ·
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11

Graduate What is the Tangent Space to the Unitary Group?

  • Kreizhn
  • · Replies 16 ·
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16

Graduate When is a foliated manifold a fibre bundle?

  • center o bass
  • · Replies 5 ·
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5