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

Undergrad Analytic Geometry - finding the normal vector at a point

  • cfphys
  • · Replies 3 ·
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3

Graduate Is classical differential geometry still useful?

  • petergreat
  • · Replies 1 ·
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1

Graduate Question about smoothness of a vector field (Reeb).

  • quasar987
  • · Replies 11 ·
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11

Graduate Definition of a homeomorphism between topological spaces

  • RedX
  • · Replies 10 ·
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10

Graduate Intersection of Connected Sets: True or False?

  • beetle2
  • · Replies 7 ·
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7

Graduate I have some trouble with the fourth spatial dimension

  • TubbaBlubba
  • · Replies 2 ·
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2

Graduate Differential Geometry: Coordinate Patches

  • SNOOTCHIEBOOCHEE
  • · Replies 1 ·
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1

High School Area of standard-sized dartboard?

  • moonman239
  • · Replies 5 ·
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5

Graduate Relationship between Diffeomorphism and Jacobian

  • RedX
  • · Replies 12 ·
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12

High School What Defines a Straight Line?

  • tauon
  • · Replies 7 ·
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7

Graduate Area of circle using incribed polygons

  • Jamin2112
  • · Replies 11 ·
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11

Graduate Laplacian of 2-Form in R^3: Reference & Calculation

  • haushofer
  • · Replies 4 ·
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4

Graduate Closure of a one-parameter subgroup

  • eok20
  • · Replies 1 ·
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1

Graduate Conformally Flat and Einstein Geometry

  • charlynd
  • · Replies 4 ·
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4

Graduate Equivalence Relations on [0,1]x[0,1] and Hausdorff Spaces

  • lttlbbygurl
  • · Replies 2 ·
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2

Graduate Lie derivative versus covariant derivative

  • RedX
  • · Replies 3 ·
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3

Graduate Ans: Is [-4.4] & (-3,3) open/closed in (ℝ,τ)? Justify your answer

  • blbl
  • · Replies 2 ·
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2

Graduate Differentiable structures and diffeomorphisms

  • RedX
  • · Replies 5 ·
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5

Graduate K-connectedness and the homotopy-lifting property

  • Bacle
  • · Replies 1 ·
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1

Graduate How to prove these with Integral Theorems

  • Gameowner
  • · Replies 3 ·
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3

Graduate Le: Tensor of Cochain Complexes, Isomorphism of Complexes

  • Bacle
  • · Replies 18 ·
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18

Graduate Is the Continuum Hypothesis Valid if the Interval is Wrapped into a Semi-Circle?

  • TheAlkemist
  • · Replies 2 ·
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2

Graduate Definition of boundary point and equation

  • wayneckm
  • · Replies 9 ·
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9

Graduate Continuous bijection that is not an embedding

  • Bacle
  • · Replies 8 ·
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8

Graduate Exterior Derivative Explained: Motivation & Calculation

  • Terilien
  • · Replies 18 ·
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18

Graduate Why Does an Isometry Preserve Lie Brackets Between Vector Fields?

  • rafax
  • · Replies 1 ·
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1

Graduate Proving the Inverse Function Theorem: A Struggle

  • lttlbbygurl
  • · Replies 1 ·
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1

Graduate Differential Geom.: Dual Space Bases for Beginners

  • nklohit
  • · Replies 8 ·
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8

Graduate Residue calculus and gauss bonnet surfaces

  • zwoodrow
  • · Replies 5 ·
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5

Graduate What Is a Quotient Bundle?

  • Bacle
  • · Replies 8 ·
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8

Graduate Why Is This Iterated Integral Expression a Homotopy Invariant?

  • lavinia
  • · Replies 1 ·
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1

Graduate Uniform continuity in top. spaces

  • Bleys
  • · Replies 5 ·
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5

Graduate Request: Solved Problems in R.Geometry; Connections, etc.

  • WWGD
  • · Replies 3 ·
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3

Graduate Lie algebra of the diffeomorphism group of a manifold.

  • eok20
  • · Replies 7 ·
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7

Graduate Compute Euler Characteristic from Z Homology Dimensions

  • lavinia
  • · Replies 4 ·
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4

Graduate Tangent map, gauss map, and shape operator

  • badgers14
  • · Replies 1 ·
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1

Undergrad Postulates that Euclid neglected to mention?

  • LeonhardEuler
  • · Replies 2 ·
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2

Graduate Are functionals united with the vector space which they operate on?

  • jaketodd
  • · Replies 9 ·
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9

Graduate Is Parallel Transport Invariance Maintained in General Relativity Calculations?

  • bueller11
  • · Replies 10 ·
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10

Graduate No difference between covectors and functions?

  • mordechai9
  • · Replies 4 ·
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4

Graduate Exterior Derivative: Proving d^2 = 0 and d(w1 wedge w2) Properties

  • jem05
  • · Replies 6 ·
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6

Graduate Global Section of Fiber Bundles with Contractible Fiber

  • MagmaMorphic
  • · Replies 2 ·
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2

Graduate Fundamental group to second homology group

  • lavinia
  • · Replies 2 ·
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2

Graduate Proof of Real Projective Plane Embedding in R4

  • rainwyz0706
  • · Replies 2 ·
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2

Graduate What is the connection between topology and convergence in probability?

  • wayneckm
  • · Replies 5 ·
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5

Graduate Intro to elementary index notation

  • fantispug
  • · Replies 1 ·
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1

Graduate Neumann boundary conditions on S^1/Z_2

  • AntideSitter
  • · Replies 3 ·
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3

Graduate What is the concept of exact forms on a 2 torus and how can it be visualized?

  • lavinia
  • · Replies 2 ·
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2

Graduate Math of Transfinite Donuts in 3-D Space

  • HarryWertM
  • · Replies 4 ·
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4

Graduate What's the difference between differential topology and algebraic topology?

  • petergreat
  • · Replies 5 ·
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5

Graduate Quotient Spaces/Homeomorphic spaces?

  • sutupidmath
  • · Replies 1 ·
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1

Undergrad Graphing Surfaces with Non-Linear Equations: What Are My Options?

  • aarciga
  • · Replies 2 ·
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2

Graduate Understanding Exterior Products of Multiple Vectors

  • jostpuur
  • · Replies 18 ·
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18

Graduate Can a Symmetric Tensor on a Manifold of Signature -+++ be Written in p-forms?

  • Phrak
  • · Replies 8 ·
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8

Graduate Help me learn the GR cartan formalism

  • zwoodrow
  • · Replies 2 ·
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2

Graduate Learn Conical Coordinates with Mathworld

  • TheDestroyer
  • · Replies 3 ·
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3

Graduate Fundamental group with n holes

  • madness
  • · Replies 8 ·
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8

Graduate Proof of Homeomorphism: An Example

  • beetle2
  • · Replies 4 ·
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4

Graduate Why Use 'Singular' to Describe Singular Simplex?

  • navigator
  • · Replies 3 ·
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3

Graduate Fundamental Group of (X,p): D^2\{(x,0) : 0<=x<=1}

  • Mikemaths
  • · Replies 3 ·
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3

Graduate What is the significance of Pi1(X,x) in understanding the fundamental group?

  • Zetta
  • · Replies 19 ·
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19

Graduate Apparent Contradiction: Every Map from a Contractible Space to any X is trivi

  • Bacle
  • · Replies 9 ·
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9

Graduate Finite Complement Topology: Why It's the Finest

  • beetle2
  • · Replies 4 ·
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4

Graduate What is the boundary of a surface?

  • quasar987
  • · Replies 15 ·
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15

Graduate What Does the Homology Group Tell Us About a Manifold?

  • Sumanta
  • · Replies 4 ·
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4

Graduate Generic Intersection of non-planar Surfaces in R^4

  • Bacle
  • · Replies 2 ·
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2

Graduate What is the role of the transpose matrix in tensor transformations?

  • peterjaybee
  • · Replies 8 ·
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8

Undergrad Why Use Open and Closed Sets in Mathematical Proofs?

  • wayneckm
  • · Replies 8 ·
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8

Graduate Homology of CP^1, complex projective 1-space

  • Bacle
  • · Replies 1 ·
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1

Graduate Relation between Frenet-Serret torsion and the torsion tensor?

  • lucyk
  • · Replies 2 ·
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2

Graduate Levi-civita connection assumptions

  • RedX
  • · Replies 1 ·
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1

Graduate Identifying tiles in hyperbolic space?

  • Coin
  • · Replies 3 ·
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3

Graduate For M a 4-mfld., every class in H_2(M;Z) can be represented by a Surface.

  • Bacle
  • · Replies 13 ·
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13

Undergrad Equations for tangent & normal at P2 of circle P1 P2 P3?

  • CosmicVoyager
  • · Replies 3 ·
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3

Graduate Shortest arc between two points in polar coordinates

  • mnb96
  • · Replies 5 ·
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5

Graduate Geometric description of (simplicial)homologous cycles

  • Bacle
  • · Replies 6 ·
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6

Graduate Orientability of Complex Manifolds.

  • Bacle
  • · Replies 6 ·
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6

Graduate What is the difference between a manifold and a metric space?

  • RedX
  • · Replies 24 ·
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24

Graduate An intuitive explanation to the Killing equation?

  • kvf
  • · Replies 2 ·
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2

Graduate Connected Spaces: Disjoint Unions & Inf Sets

  • Mikemaths
  • · Replies 5 ·
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5

Graduate Need assistance,can you imagine a continuously deformation between X and Y?

  • kakarotyjn
  • · Replies 1 ·
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1

Undergrad Hyperbolic Geometry: Euclidean v 4D in 3D Space

  • Praxisseiz
  • · Replies 2 ·
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2

Graduate How to make curved line into torus?

  • CosmicVoyager
  • · Replies 1 ·
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1

Graduate Represntative Surfaces/Curves in homology. Examples.?

  • Bacle
  • · Replies 7 ·
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7

Graduate Easy-to-Follow Proofs for Symplectic Manifolds: A Comprehensive Resource

  • Nusc
  • · Replies 9 ·
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9

Graduate Understanding Contractible Spaces: Path Connected vs Simply Connected

  • madness
  • · Replies 11 ·
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11

Graduate Understanding the Square Root Loop and Its Construction on S^1 and RP^1

  • madness
  • · Replies 5 ·
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5

Graduate Sphere as an embedded submanifold

  • jem05
  • · Replies 6 ·
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6

Undergrad Definition of a line between two points on a sphere

  • TravelGirl
  • · Replies 13 ·
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13

High School Definition of the Cross Product?

  • 2^Oscar
  • · Replies 11 ·
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11

Undergrad How Does Horizontal Deviation Affect Elliptical Projection of a Sphere?

  • Chandi
  • · Replies 1 ·
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1

Undergrad How Can You Calculate the Distance Between Two Pulley Centers Using Belt Length?

  • itchy8me
  • · Replies 18 ·
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18

Graduate Is it possible to prove that any metric topology is Hausdorff?

  • sutupidmath
  • · Replies 4 ·
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4

Graduate Curl of the transpose of a gradient of a vector: demonstration of an identity

  • traianus
  • · Replies 15 ·
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15

Graduate Understanding Lie Derivatives: Acting on Vectors & Tensors

  • linford86
  • · Replies 8 ·
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8

Graduate Contraction map of geometric mean

  • rubinj
  • · Replies 2 ·
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2

Graduate Number of independent subcubes of a hypercube

  • twoflower
  • · Replies 1 ·
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1

Graduate Translation in Spherical Coordinates

  • karanmohan
  • · Replies 1 ·
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1

Graduate Can a Metric be Defined to Make All Balls in R^2 Unbounded with Shrinking Radii?

  • jostpuur
  • · Replies 7 ·
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7

Graduate Mobius Band as Bundle Over S^1: Trivialization Containing (1,0) in S^1

  • WWGD
  • · Replies 5 ·
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5