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 What is a Twistor: Explaining Geometric Applications

  • mnb96
  • · Replies 10 ·
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10

Graduate Differing definitions of an inner product

  • Kreizhn
  • · Replies 4 ·
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4

Graduate Tychonoff's theorem and convergent subsequence

  • Monocles
  • · Replies 11 ·
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11

Graduate Is Jurdjevic's Definition of Differential Forms an Alternative Approach?

  • Kreizhn
  • · Replies 3 ·
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3

Graduate Interpreting Intersection Form in H_1(K)

  • Bacle
  • · Replies 13 ·
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13

Graduate Vector field as smooth embedding

  • huyichen
  • · Replies 2 ·
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2

Graduate Hausdorff dimension of the Cantor Set

  • alpar_r
  • · Replies 1 ·
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1

Graduate Why Do We Minimize the Squared Length in Surface Distance Calculations?

  • Noxide
  • · Replies 1 ·
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1

Graduate Calculate point on line, perpendicular and intersecting another line in 3d space

  • WLamers
  • · Replies 1 ·
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1

Graduate Finding the Metric in Stereographic Projection

  • mnb96
  • · Replies 8 ·
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8

Graduate What Is the Geometric Difference in Intersection Forms Q(a,b) vs Q(b,a)?

  • WWGD
  • · Replies 0 ·
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0

Graduate Zero curvature => straight line proof

  • Shaybay92
  • · Replies 1 ·
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1

Graduate Nonvanishing section for direct sum of Mobius band

  • huyichen
  • · Replies 1 ·
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1

Graduate How to show that a transverse intersection is clean, but not conversely?

  • huyichen
  • · Replies 4 ·
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4

Graduate Are Metric Space Infimums Equal for Non-Empty Subsets?

  • choccookies
  • · Replies 4 ·
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4

Undergrad Working with different coordinate systems

  • koab1mjr
  • · Replies 1 ·
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1

Graduate Example of Codimension-1 Manifolds that are not Isotopic.?

  • Bacle
  • · Replies 2 ·
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2

Graduate What is the fundamental group of X?

  • quasar987
  • · Replies 11 ·
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11

Graduate The Codimension of a singularity

  • Kreizhn
  • · Replies 4 ·
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4

Graduate About the coherent topology wiki page

  • quasar987
  • · Replies 1 ·
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1

Graduate Is the One-Form d \theta Well-Defined at the North and South Pole on a 2-Sphere?

  • rbayadi
  • · Replies 5 ·
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5

Graduate What does it mean for a change of variables to be UNITARY?

  • AxiomOfChoice
  • · Replies 2 ·
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2

Graduate Exponential Map of R3: A Closer Look

  • enricfemi
  • · Replies 4 ·
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4

Graduate Can Odd Degree Maps from S^3 to RP^3 Be Constructed Smoothly?

  • owlpride
  • · Replies 20 ·
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20

Graduate Is the Closed Unit Square Homeomorphic to the Closed Unit Disc?

  • metder
  • · Replies 3 ·
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3

Graduate What is the surface parametrization for rotating y=Cosh(x) about the x-axis?

  • chaotixmonjuish
  • · Replies 2 ·
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2

Graduate Integration in Sean Carroll's parallel propagator derivation

  • Rasalhague
  • · Replies 2 ·
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2

Graduate Finsler Geometry: What is the Quadratic Restriction?

  • math6
  • · Replies 2 ·
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2

Graduate Defining Metrics on Submanifolds: Is G = goi* a Valid Approach?

  • math6
  • · Replies 2 ·
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2

Graduate What is the meaning of constant on each others fibres in differential geometry?

  • Kreizhn
  • · Replies 9 ·
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9

Graduate If I want to learn about tensor mathematics - where do I need to start

  • mtc1973
  • · Replies 3 ·
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3

Graduate Point Set Topology: Non-Trivial Facts Beyond Uryshon's Lemma

  • facenian
  • · Replies 5 ·
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5

Graduate Can We Define the Tangent Bundle of a Vector Space V?

  • math6
  • · Replies 2 ·
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2

Graduate Definition of a sub-elliptic differential operator

  • math6
  • · Replies 2 ·
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2

Graduate How Accurate Is the Spherical Law of Cosines for Calculating Distances?

  • moonman239
  • · Replies 1 ·
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1

Graduate Is every one-dimensional manifold orientable?

  • racoonlly
  • · Replies 1 ·
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1

Graduate Covariant derivate same as normal derivative?

  • vitaniarain
  • · Replies 3 ·
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3

Graduate How to show 2-tori is diffeomorphic to S^3

  • robforsub
  • · Replies 4 ·
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4

Graduate Trouble with Algebraic Geometry in General

  • Newtime
  • · Replies 9 ·
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9

Undergrad How does a matrix indicate a point?

  • mynameinc
  • · Replies 6 ·
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6

Graduate Covariant derivative of the metric

  • vitaniarain
  • · Replies 3 ·
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3

Graduate Proving F is an Isometry for C^1 Functions in Elementary Geometry

  • MathematicalPhysicist
  • · Replies 5 ·
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5

Graduate Orientation preserving reparameterization

  • chaotixmonjuish
  • · Replies 2 ·
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2

Graduate Let M be a manifold and g a metric over M

  • math6
  • · Replies 5 ·
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5

Graduate What is the Unknown Theorem Used in the Proof of Theorem 4.5?

  • Noxide
  • · Replies 5 ·
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5

Graduate Combining 3D Angles: A Quaternions Solution?

  • Twinbee
  • · Replies 7 ·
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7

Undergrad Is There a Map Projection Where Distances Remain Constant at All Latitudes?

  • DaveC426913
  • · Replies 2 ·
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2

Graduate How Does Compactness Affect Function Behavior in Metric Spaces?

  • wayneckm
  • · Replies 5 ·
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5

Undergrad Object and a 3d direction vector

  • badescuga
  • · Replies 1 ·
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1

Undergrad What are the Functions of Riemann Invariants?

  • lavster
  • · Replies 1 ·
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1

Graduate Curvilinear & Cartesian Conversions

  • G4CKT
  • · Replies 1 ·
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1

Graduate Non-linear forms & tensor densities

  • Rasalhague
  • · Replies 14 ·
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14

Graduate Is This Special Case of Stokes Theorem True?

  • paweld
  • · Replies 8 ·
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8

Graduate 4d Cartesian to Polar Transform

  • chasehusky
  • · Replies 1 ·
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1

Graduate Understanding Covariant Derivative: d Explained

  • TromboneNerd
  • · Replies 8 ·
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8

Graduate 3D object inverted w.r.t. a sphere

  • neelakash
  • · Replies 1 ·
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1

Undergrad Finding normal vector on circles

  • _Seven_
  • · Replies 2 ·
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2

Graduate Topology and Euler Classes of Oriented 2-Plane Bundles in R^4

  • lavinia
  • · Replies 13 ·
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13

Undergrad How do I calculate straight line distance on a sphere?

  • G4CKT
  • · Replies 6 ·
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6

Graduate How Can I Determine Sphere Orientation During Rotation?

  • _Seven_
  • · Replies 2 ·
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2

Graduate Simple identity for antisymmetric tensor

  • paweld
  • · Replies 4 ·
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4

Graduate How to Prove the Cartan Tensor in SM?

  • math6
  • · Replies 2 ·
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2

Graduate Problem in Topology: Disjoint Cover of Closed Subsets

  • disregardthat
  • · Replies 15 ·
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15

Graduate Is f' continuous when removing elements from X and Y?

  • radou
  • · Replies 22 ·
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22

Graduate Intersection of complex sphere and cone

  • huyichen
  • · Replies 1 ·
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1

Graduate Number of Nondegenerate Zeros of Vector Field Bounded

  • huyichen
  • · Replies 2 ·
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2

Graduate Can a Center of a Sphere be conceived at infinity

  • neelakash
  • · Replies 6 ·
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6

Undergrad Nosecone Geometry: Tri-Conic & Bi-Conic

  • sorter
  • · Replies 1 ·
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1

Graduate Proving a product of compact spaces is compact

  • radou
  • · Replies 2 ·
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2

Graduate Octonians (new paper by Louis Kauffman and Jon Hackett)

  • marcus
  • · Replies 16 ·
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16

Undergrad Hyperbola conjugate,a>b questions

  • sachin123
  • · Replies 6 ·
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6

Graduate How to prove that a given set is a torus

  • glmuelle
  • · Replies 3 ·
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3

Graduate Smooth covering map and smooth embedding

  • huyichen
  • · Replies 1 ·
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1

Undergrad How can understanding metric space help with real-world problems?

  • fireboy420
  • · Replies 3 ·
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3

Undergrad Finding Multiple Right Inverses: A Quick Guide

  • fireboy420
  • · Replies 1 ·
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1

Graduate What is the Gaussian Curvature of a Cone at its Vertex?

  • lavenderblue
  • · Replies 7 ·
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7

Graduate A path connected product of path connected spaces

  • radou
  • · Replies 6 ·
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6

Undergrad How this equation represent the equation of line?

  • Hyperspace2
  • · Replies 4 ·
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4

Undergrad Seeking help with visualizing surface

  • Kmenex
  • · Replies 1 ·
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1

Graduate Defining a manifold without reference to the reals

  • bcrowell
  • · Replies 25 ·
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25

Graduate Definition of 2D Biquadratic Surface - 65 Characters

  • Shaddyab
  • · Replies 3 ·
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3

Graduate Is the Euclidean Metric on RxR and C a Valid Metric?

  • fabbi007
  • · Replies 1 ·
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1

Graduate Is EndE Linear with Respect to c ^ ∞ (B)?

  • math6
  • · Replies 1 ·
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1

Undergrad Positioning B at the distance dz from A

  • onako
  • · Replies 1 ·
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1

Graduate Hamiltonian Flow: Meaning & Definition

  • Rasalhague
  • · Replies 2 ·
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2

Graduate Proving Pushforward Product Isomorphism: M1 x ... x Mk to M1 + ... + Mk

  • robforsub
  • · Replies 3 ·
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3

Graduate Why Is the Heine-Borel Theorem Unique to ℝ?

  • Buri
  • · Replies 14 ·
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14

Graduate Smooth manifold and constant map

  • huyichen
  • · Replies 2 ·
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2

Graduate What Are the Key Concepts in Alexei Kovalev's Article on Vector Subspaces?

  • math6
  • · Replies 9 ·
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9

Graduate Vector fields in cylindrical and spherical coordinates

  • arkajad
  • · Replies 14 ·
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14

Graduate What is the relationship between topology and convergence in defining open sets?

  • wayneckm
  • · Replies 1 ·
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1

Graduate How to Find Conveniently Spaced Unit Vectors in N-Dimensions?

  • Gerenuk
  • · Replies 2 ·
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2

Undergrad Calculate coordinate in 3D triangle.

  • pjhphysics
  • · Replies 2 ·
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2

Graduate Vertical and horizontal subspace

  • math6
  • · Replies 12 ·
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12

Graduate Vertical and horizontal subspace of a vector space T_pP.

  • wdlang
  • · Replies 9 ·
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9

Graduate Bundle morphisms and automorphism

  • math6
  • · Replies 12 ·
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12

Graduate Probability measure on smooth functions

  • Tac-Tics
  • · Replies 2 ·
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2

Graduate What would a 3D ball look like (in 3D) if it were partially in 4D space?

  • Diffused
  • · Replies 7 ·
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7

Graduate Simple Applications of Noncommutative Geometry?

  • LukeD
  • · Replies 3 ·
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3

Graduate Differences between Algebraic Topology and Algebraic Geometry

  • annoymage
  • · Replies 2 ·
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2