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 Theorems every mathematician should know

  • jgm340
  • · Replies 83 ·
3
Replies
83

Undergrad Layperson asking about circle sides (Warning may not make sense)

  • joebloggs
  • · Replies 7 ·
Replies
7

Graduate How do we interpret the differential of a function on a smooth manifold?

  • panzervlad
  • · Replies 2 ·
Replies
2

Graduate Math Student Struggling with Griffiths Harris Algebraic Geometry

  • Kalidor
  • · Replies 13 ·
Replies
13

Graduate Understanding the Gauss Bonnet Theorem for 2D Riemann Surfaces

  • lavinia
  • · Replies 1 ·
Replies
1

Graduate Mathematician Wins Abel Prize for Exotic 7-Dimensional Spheres

  • ATranPV
  • · Replies 1 ·
Replies
1

High School Triangle and two circles theorem

  • Delong
  • · Replies 3 ·
Replies
3

Graduate Natural Metrics on (Special) Unitary groups.

  • Kreizhn
  • · Replies 2 ·
Replies
2

Graduate Did I Make a Mistake in Computing the Gradient on a Unitary Group?

  • Kreizhn
  • · Replies 4 ·
Replies
4

Graduate Optimizing Volume of a Rectangle with Newton's Method?

  • EngWiPy
  • · Replies 2 ·
Replies
2

Graduate What is the relationship between phase space and space-time?

  • Loren Booda
  • · Replies 1 ·
Replies
1

Graduate Proof that Fin.-Gen. Group G is Fund. Group of 2-Cell Complex

  • Bacle
  • · Replies 2 ·
Replies
2

Graduate Total absolute curvature of a compact surface

  • Goklayeh
  • · Replies 12 ·
Replies
12

Undergrad Help on Ellipse Example 5.4L - Understand m1 & m2

  • Michael_Light
  • · Replies 1 ·
Replies
1

Graduate Augmented reality rotation & zoom

  • tyrskyzz
  • · Replies 1 ·
Replies
1

Graduate (anti)-symmetries of the Riemann curvature tensor

  • quasar987
  • · Replies 5 ·
Replies
5

Graduate Understanding Tangent Map Derivation in S.S. Chern's Ebook

  • Sumanta
  • · Replies 1 ·
Replies
1

Graduate What does it mean by a Riemannian metric on a vector bundle?

  • petergreat
  • · Replies 9 ·
Replies
9

Graduate Invariant Polynomials on complexified bundles with connection

  • lavinia
  • · Replies 0 ·
Replies
0

Graduate Principle Fibre: Definition & Examples

  • RoboticMezon
  • · Replies 7 ·
Replies
7

Graduate Theorema Egregium: Does Gauss's Theorem Generalize?

  • lavinia
  • · Replies 2 ·
Replies
2

Graduate Hypersurfaces of Euclidean space

  • lavinia
  • · Replies 1 ·
Replies
1

Graduate Why Does Parallel Transport on a Circle Cause Vector Field Rotation?

  • murmillo
  • · Replies 1 ·
Replies
1

Graduate Lie-algebraic elements as derivations.

  • Kreizhn
  • · Replies 1 ·
Replies
1

Graduate Eigenvalues of the Frenet formulas and angular velocity

  • ForMyThunder
  • · Replies 1 ·
Replies
1

Graduate What is the Acyclic Carrier Theorem and how can it be applied using chain maps?

  • Socrates' Pen
  • · Replies 2 ·
Replies
2

Graduate Quotient Map Theorem: Topology Induced by f

  • ForMyThunder
  • · Replies 5 ·
Replies
5

Is there any specific name for a coffee cup handle in mathematics?

  • princy
  • · Replies 10 ·
Replies
10

Graduate Radius of Ellipsoid with Known a,b,c and Phi, Theta

  • WhyIsItSo
  • · Replies 13 ·
Replies
13

Graduate Axiom of Abelian Category: AB5 & AB5*

  • jose80
  • · Replies 1 ·
Replies
1

Graduate Is There a Theorem for Fibration Over R for Non-Compact Manifolds?

  • holy_toaster
  • · Replies 4 ·
Replies
4

Graduate How to express a circle in spherical coordinates

  • TBTTyler
  • · Replies 4 ·
Replies
4

Graduate Can 2-Spheres Exist in 2D Slices of 3D Space?

  • TrickyDicky
  • · Replies 7 ·
Replies
7

High School Naming Concentric Circles: What's the Best Approach?

  • faiz4000
  • · Replies 5 ·
Replies
5

Graduate Dual vector bundle E* is isomorphic to Hom(E, MXR)

  • robforsub
  • · Replies 4 ·
Replies
4

Undergrad Solve Manhattan Dist. Equation for 2D Line AB, Point C

  • onako
  • · Replies 1 ·
Replies
1

Undergrad Quaternions and rotation vector.

  • pjhphysics
  • · Replies 4 ·
Replies
4

Graduate How can 3D space expand and contract without a fourth dimension?

  • Feeble Wonk
  • · Replies 1 ·
Replies
1

Undergrad How Can a Grade 12 Student Progress to Advanced Geometry?

  • mathsTKK
  • · Replies 6 ·
Replies
6

Graduate New Model for Flocking Behavior: S. Motsch & E. Tadmor

  • marcus
  • · Replies 0 ·
Replies
0

Undergrad How Do You Apply the Intermediate Value Theorem to Various Intervals on a Graph?

  • null(0)
  • · Replies 1 ·
Replies
1

Graduate How Does Gauss Curvature Integral Relate to Holonomy in SO(2) Bundles?

  • lavinia
  • · Replies 0 ·
Replies
0

Undergrad Finding a second point on a circle

  • chuckrussell
  • · Replies 3 ·
Replies
3

Graduate Is this Matrix a Tensor, Pseudotensor, or Neither?

  • Marthius
  • · Replies 2 ·
Replies
2

Graduate Finding Convex Hulls in hyperbolic spaces

  • Hyperbolful
  • · Replies 4 ·
Replies
4

Graduate Caustic Curves and Dual Curves: Are They Different?

  • mdoni
  • · Replies 3 ·
Replies
3

Graduate What are the best books to learn topology and representation theory?

  • linkedlister
  • · Replies 11 ·
Replies
11

Graduate Riemannian Manifold: Integral Formula Explained

  • whattttt
  • · Replies 1 ·
Replies
1

Graduate Can the integral of W^dV be interpreted as a linking number in projective space?

  • lavinia
  • · Replies 4 ·
Replies
4

Graduate What is the Physical Meaning of Circulation in Vector Fields?

  • Curl
  • · Replies 2 ·
Replies
2

Graduate How to Find the Length of a Circle on a Unit Sphere?

  • whattttt
  • · Replies 5 ·
Replies
5

Graduate Are Rotations Exponential? Understanding the Concepts Behind Euler Identity

  • Opus_723
  • · Replies 1 ·
Replies
1

Graduate Prove Compact Surface: Alg. Topology Help with Polygon Sides Identification

  • sutupidmath
  • · Replies 3 ·
Replies
3

Graduate Another proof that a vector field on the sphere must have a zero?

  • lavinia
  • · Replies 41 ·
2
Replies
41

Graduate How to Find the Length of a Circle on the Unit Sphere?

  • whattttt
  • · Replies 1 ·
Replies
1

Graduate Parametrizations and regular curves

  • Buri
  • · Replies 9 ·
Replies
9

Graduate Definition of the gradient operator

  • elgen
  • · Replies 2 ·
Replies
2

Graduate Show that there exists no sequence of functions satisfying the following

  • poet_3000
  • · Replies 3 ·
Replies
3

Graduate How to make a hodge dual with no metric, only volume form

  • camel_jockey
  • · Replies 3 ·
Replies
3

Graduate Understanding Knots in Higher Dimensions

  • oldman
  • · Replies 10 ·
Replies
10

Graduate Solve Geodesic Problem for f:[a,b] to R

  • wii
  • · Replies 3 ·
Replies
3

Graduate Confused with closure and interior

  • Damascus Road
  • · Replies 4 ·
Replies
4

Graduate What is the intuitive explanation for the homology of S^3\knot?

  • pp31
  • · Replies 2 ·
Replies
2

Graduate Euclidean Killing Field Question

  • Kreizhn
  • · Replies 1 ·
Replies
1

Graduate Please help. Imposing a metric to preserve distance

  • whattttt
  • · Replies 2 ·
Replies
2

Graduate Convergence in the product and box topology

  • calvin22
  • · Replies 1 ·
Replies
1

Undergrad What Does Preserving Distance Mean in Metric Mapping?

  • whattttt
  • · Replies 2 ·
Replies
2

Graduate Proving Measure Zero for Set A Derived from Real Numbers Set E

  • arvindam
  • · Replies 3 ·
Replies
3

Graduate Homeomorphism classes of compact 3-manifolds

  • pp31
  • · Replies 2 ·
Replies
2

Graduate Compactness in Metric Spaces: Is It Possible?

  • Bleys
  • · Replies 2 ·
Replies
2

Undergrad Is Geometry a Branch of Physics?

  • pmb_phy
  • · Replies 49 ·
2
Replies
49

Graduate Elliptic Trig: Circles, Hyperbolas & Ellipses

  • JyN
  • · Replies 6 ·
Replies
6

Graduate Lower Limit Topology: Explaining Lemma 13.4 of Munkres' Topology

  • princy
  • · Replies 6 ·
Replies
6

Graduate Compactness of Tangent Bundle: Manifold M

  • math6
  • · Replies 9 ·
Replies
9

Graduate Relationship between radius of curvature and slope

  • bpcraig
  • · Replies 5 ·
Replies
5

Undergrad Graphing θ=π/4 in Polar Coordinates

  • shayaan_musta
  • · Replies 6 ·
Replies
6

Graduate Troubleshooting Lie Brocket Connection Issues

  • wii
  • · Replies 8 ·
Replies
8

Graduate Why does removing a submanifold of codim 2 preserve connectivity?

  • HMY
  • · Replies 7 ·
Replies
7

Undergrad Closest approach of line segments

  • Lindley
  • · Replies 2 ·
Replies
2

Graduate How to Compute r in Stereographic Projection from R^4 to R^3?

  • whattttt
  • · Replies 3 ·
Replies
3

Graduate Find Shortest Distance to Point on Ellipsoid

  • golmschenk
  • · Replies 2 ·
Replies
2

Graduate Intersection of plane in spherical coordinate system

  • foruforewer
  • · Replies 1 ·
Replies
1

Graduate S^5 Sphere: Visualizing and Understanding

  • yola
  • · Replies 4 ·
Replies
4

Graduate Complex-valued functions on a compact Hausdorff space.

  • Fredrik
  • · Replies 24 ·
Replies
24

Undergrad Geometric construction of the square root

  • JeremyEbert
  • · Replies 4 ·
Replies
4

Graduate Topology (specifically homotopy) question

  • timboj2008
  • · Replies 3 ·
Replies
3

Graduate Coordinate basis vs local frame?

  • pellman
  • · Replies 2 ·
Replies
2

Graduate Harmonic forms on resolved toric calabi yau spaces

  • wodhas
  • · Replies 1 ·
Replies
1

Graduate Finite Rank Operators: Prove T* Has Finite Rank

  • Fredrik
  • · Replies 14 ·
Replies
14

Graduate How accessible is Bott & Tu's book on algebraic topology?

  • petergreat
  • · Replies 5 ·
Replies
5

Graduate Help for proving a mapping is a diffeomorphism

  • whattttt
  • · Replies 9 ·
Replies
9

Graduate Solve that without 4th order polynomial?

  • Gerenuk
  • · Replies 9 ·
Replies
9

Graduate Perspective sketches from 4D to 3D?

  • Curl
  • · Replies 2 ·
Replies
2

Undergrad What is the angle between a disc and a vertical surface?

  • con20or
  • · Replies 1 ·
Replies
1

Graduate Compact n-manifolds as Compactifications of R^n

  • Bacle
  • · Replies 4 ·
Replies
4

Graduate Del operator with coordinate transformations

  • Curl
  • · Replies 7 ·
Replies
7

Graduate Confusion on the definition of a quotient map

  • Esran
  • · Replies 2 ·
Replies
2

Graduate How do symplectic manifolds describe kinematics/dynamics ?

  • camel_jockey
  • · Replies 3 ·
Replies
3

Graduate What is the meaning of C^r-close in topological terms?

  • quasar987
  • · Replies 2 ·
Replies
2

Graduate Theory of calculating sphere centres from surface co-ordinates

  • broouk
  • · Replies 2 ·
Replies
2