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 Understand differentiable manifolds

  • goksen
  • · Replies 3 ·
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3

Graduate What determines the number of differentiable structures on a manifold?

  • matness
  • · Replies 15 ·
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15

Graduate Can You Explain the Meaning of the Affine Connection in Simple Terms?

  • the shadow
  • · Replies 12 ·
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12

Graduate Tangent vectors in affine spaces

  • mma
  • · Replies 9 ·
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9

Graduate What is the relationship between differential forms and degree?

  • KarateMan
  • · Replies 8 ·
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8

Graduate How can we prove path connectedness and disconnectedness of certain groups?

  • MathematicalPhysicist
  • · Replies 10 ·
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10

Graduate Proving Geodesic Pushed by Isometric Diffeomorphism

  • CompuChip
  • · Replies 4 ·
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4

Graduate Theorem Egregium: Intrinsic Extrinsic Gauss Curvature of 3D Surfaces

  • wofsy
  • · Replies 5 ·
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5

Graduate What is the significance of immersions and embeddings in the study of manifolds?

  • Cincinnatus
  • · Replies 8 ·
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8

Graduate What Is the Dual Space in Spivak's Calculus on Manifolds?

  • Peeter
  • · Replies 9 ·
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9

Graduate Preparing for Differential Geometry Class: Basics to Know

  • sparkster
  • · Replies 22 ·
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22

Graduate Number of zeros of (tangent) vector field on sphere

  • justincase
  • · Replies 6 ·
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6

Graduate What Does the Dirac Delta Function Look Like in Curved Spacetime?

  • friend
  • · Replies 6 ·
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6

Graduate Convert flat space function to curved space function?

  • friend
  • · Replies 5 ·
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5

Undergrad The widest point on an ellipsoid

  • only_huce
  • · Replies 6 ·
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6

Graduate Understanding the Difference between Scalar and Dot Product in Tensor Calculus

  • matheinste
  • · Replies 4 ·
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4

Graduate Advisement on 4-manifolds: please suggest

  • WWGD
  • · Replies 10 ·
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10

Graduate Reconciling Differential Forms Inner Product of Wedge with GA Dot

  • Peeter
  • · Replies 6 ·
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6

Graduate How Do You Calculate Ray and Ellipsoid Intersections?

  • bobthebanana
  • · Replies 2 ·
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2

Graduate Differential modulo another differential

  • astros
  • · Replies 2 ·
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2

Undergrad Finding the Normal to a Plane Using Vector Geometry

  • bobmoin
  • · Replies 1 ·
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1

Graduate Can a point on any 2d surface be uniquely identified by only 2 coordinates?

  • Werg22
  • · Replies 10 ·
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10

Graduate Classification Theorem of Surfaces

  • Tchakra
  • · Replies 8 ·
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8

Graduate How to prove a function is an isometry

  • Cincinnatus
  • · Replies 4 ·
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4

Graduate What is the Difference Between a Lie Subalgebra and a Subspace?

  • KarateMan
  • · Replies 5 ·
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5

Graduate Gamma How to Calculate Gamma: Step by Step

  • John Creighto
  • · Replies 2 ·
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2

Graduate Kahler Manifolds: Understanding Mutual Compatibility

  • WWGD
  • · Replies 5 ·
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5

Graduate How to Derive d^* Without Using the Hodge Star Operator?

  • HenryGomes
  • · Replies 5 ·
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5

Graduate Is My Understanding of Homotopy and the Fundamental Group Correct?

  • MathematicalPhysicist
  • · Replies 7 ·
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7

Graduate Parallel transport in flat polar coordinates

  • Damidami
  • · Replies 7 ·
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7

Graduate What Are Tensors and Their Applications in Mathematics?

  • nicksauce
  • · Replies 7 ·
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7

Graduate I am trying to figure out what exactly a dyadic is

  • gphys
  • · Replies 2 ·
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2

Find English translations of Elie Cartan's Papers

  • dx
  • · Replies 2 ·
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2

Graduate Covariant derivative of metric tensor

  • Damidami
  • · Replies 3 ·
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3

Graduate Comparing Books on Lie Groups: Representations & Compact Lie Groups

  • mrandersdk
  • · Replies 2 ·
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2

Undergrad Area of Isosceles Triangle Given Radius & Altitude

  • studof09
  • · Replies 1 ·
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1

Graduate How Can I Find Tangents on a Surface Passing Through an External Point?

  • AtulSharma
  • · Replies 6 ·
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6

Graduate Exterior Calculus and Differential Forms?

  • Phrak
  • · Replies 3 ·
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3

Graduate Is H'_n(X) Isomorphic to H_n(X, y) in Relative Singular Homology?

  • eastside00_99
  • · Replies 17 ·
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17

Graduate Tensor product commutes with pullback?

  • CompuChip
  • · Replies 3 ·
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3

Graduate Divergence of a two dimensional 3 order tensor

  • MasterD
  • · Replies 1 ·
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1

Graduate Curl or maxwell equations in higher dimensions

  • snowstorm69
  • · Replies 5 ·
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5

Graduate The space of continuous functions.

  • MathematicalPhysicist
  • · Replies 15 ·
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15

Graduate Calculating Riemannian Metric Tensor for a Vector

  • ejays
  • · Replies 5 ·
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5

Graduate Does Convergence in Open-Compact Topology Ensure Pointwise Convergence?

  • MathematicalPhysicist
  • · Replies 3 ·
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3

Graduate What happens when you multiply two simplices?

  • homomorphism
  • · Replies 6 ·
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6

Graduate Proving the Existence of Fixed Points in Compact Metric Spaces

  • MathematicalPhysicist
  • · Replies 8 ·
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8

Graduate Examples of Separation Axioms

  • MathematicalPhysicist
  • · Replies 3 ·
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3

Graduate Pascal's Triangle for non-commutative?

  • Pythagorean
  • · Replies 5 ·
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5

Graduate Serre Spectral Sequence. Motivation

  • WWGD
  • · Replies 1 ·
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1

Graduate Lie Derivative of Real-Valued Functions and Vectorfields on Manifolds

  • cliowa
  • · Replies 4 ·
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4

Graduate Rotate point on sphere to exactly 'cut sphere in half'

  • Twinbee
  • · Replies 11 ·
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11

Graduate Definition of a function by a metric.

  • MathematicalPhysicist
  • · Replies 5 ·
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5

Graduate Advice on complex analysis, Riemann surface & complex mappings.

  • Shaun Culver
  • · Replies 3 ·
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3

Graduate Normal space goes to Normal space.

  • MathematicalPhysicist
  • · Replies 2 ·
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2

Graduate What is the Connection Between Fibre Bundles and Their Components?

  • matness
  • · Replies 4 ·
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4

Graduate Understanding the Lie Derivative for Tensor Fields

  • jdstokes
  • · Replies 5 ·
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5

Graduate What Does the Bracket Operation < , > Signify in the Intersection Form Qm?

  • WWGD
  • · Replies 5 ·
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5

Graduate Proving Equivalence of Metrics Using Concavity

  • MathematicalPhysicist
  • · Replies 4 ·
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4

High School Scalar vs Vector: Explaining the Difference

  • quasar_4
  • · Replies 5 ·
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5

Graduate Prove Tensor Analysis Relation: Γᵢₖᵣ = ∊ᵢ • ∂∊ⱼ/∂qᵏ

  • Arham
  • · Replies 6 ·
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6

Undergrad Consider a surface S on which a scalar field f is defined

  • coverband
  • · Replies 5 ·
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5

Graduate Singularities and conservative vector fields

  • NewGuy
  • · Replies 2 ·
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2

Graduate What are the basics of differential topology?

  • Mystic998
  • · Replies 7 ·
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7

Undergrad Bezier curve(again): given Y, solve for X

  • abeall
  • · Replies 1 ·
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1

Graduate Topological continuity (a few questions).

  • MathematicalPhysicist
  • · Replies 4 ·
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4

Graduate Does c(t) = ((1+t,0),(0,1+t)) Provide a Counterexample on p.85 of Spivak's Book?

  • zhentil
  • · Replies 4 ·
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4

Graduate What Resources Best Translate Mathematical Tensors for Physicists?

  • dreamtheater
  • · Replies 4 ·
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4

Graduate Why Are Lie Groups Considered Manifolds?

  • Shaun Culver
  • · Replies 3 ·
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3

Graduate Which Lie Groups are Riemann Manifolds?

  • Bowles
  • · Replies 12 ·
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12

Graduate How to Prove the Magnetic Induction B from Vector Potential A Elegantly?

  • Sagreda
  • · Replies 1 ·
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1

Graduate Understanding Surface Tensors: Pauli's Theory of Relativity

  • eep
  • · Replies 4 ·
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4

Graduate Transformation of Rank 2 mixed tensor

  • cathalcummins
  • · Replies 1 ·
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1

Graduate Understanding the Gradient and Divergence of Cartesian Tensors

  • esorolla
  • · Replies 2 ·
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2

Undergrad Can You Convert a 2D Shape into 3D by Rotating It?

  • natski
  • · Replies 9 ·
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9

Graduate Non-Orthogonality of Frames Del/Delx^i ; i=1, n

  • WWGD
  • · Replies 7 ·
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7

Graduate Calculating Offsets on the Normal Coordinate System

  • chemart
  • · Replies 3 ·
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3

Graduate What is the Difference Between Vectors and Covectors?

  • cathalcummins
  • · Replies 5 ·
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5

Graduate Geodesic coordinates and tensor identities

  • haushofer
  • · Replies 11 ·
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11

Graduate Solve Gauss Curvature for Ruled Surface: A(s)+tB(s)

  • moo5003
  • · Replies 1 ·
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1

Graduate Understanding tensor contraction

  • jdstokes
  • · Replies 10 ·
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10

Graduate Frenet-Serre Frames and circles.

  • WWGD
  • · Replies 0 ·
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0

Graduate Deriving T(\theta,\tau) from Definition of $\otimes$

  • cathalcummins
  • · Replies 3 ·
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3

Graduate Help with determining Angle of Rotation for a Conic, please.

  • popsquare
  • · Replies 2 ·
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2

Graduate Are Geodesics Preserved by Diffeomorphisms of Hyperbolic Geometry?

  • WWGD
  • · Replies 8 ·
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8

Graduate Can a One Parameter Family of Metrics Be Metricizable?

  • Haelfix
  • · Replies 2 ·
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2

Graduate The Physical Significance of Tensor Product

  • captain
  • · Replies 17 ·
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17

Graduate Translation of euler angles into rotation around arbitrary axis

  • husham
  • · Replies 3 ·
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3

Graduate Non-integrable tangent distributions

  • jostpuur
  • · Replies 5 ·
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5

Graduate M-Curves: Representations & Properties of C^oo Manifolds

  • brown042
  • · Replies 6 ·
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6

Graduate Is the correct formula for curvature using the arc length parameter?

  • scottie_000
  • · Replies 2 ·
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2

Graduate Surface with Ricci scalar equal to two

  • Giammy85
  • · Replies 7 ·
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7

Graduate Can Vector Fields be Extended to Submanifolds?

  • WWGD
  • · Replies 6 ·
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6

Graduate What is the equation for helical path length around a torus?

  • BasicWill
  • · Replies 1 ·
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1

Graduate Non-Degenerate Tensors: What is the Meaning and Significance?

  • quasar_4
  • · Replies 7 ·
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7

Graduate Manifold & Metric: Does it Need a Metric?

  • princeton118
  • · Replies 4 ·
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4

Graduate How to Perform Operations on Vector Fields F and G?

  • Obstacle1
  • · Replies 3 ·
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3

Graduate Understanding Motivation of De Rham Cohomology for Manifolds

  • Cincinnatus
  • · Replies 10 ·
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10

Graduate Poincare Conjecture: Fundamental Group of V Explained

  • pivoxa15
  • · Replies 2 ·
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2

Graduate What is the Role of Lie Groups in Isometry Actions on Spaces?

  • WWGD
  • · Replies 2 ·
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2