Menu

Navigation

More options

Style variation

Contact us

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.

Filters

Geometry - Stereographic projection

Dec 19, 2005 · Replies 2 · Dec 21, 2005

Replies: 2

Views: 4K

X.Calculating the Lie Derivative of a One-Form with Respect to a Vector Field

Dec 15, 2005 · Replies 2 · Dec 19, 2005

Replies: 2

Views: 7K

Physics & Topology: Research, Books & Articles

Dec 13, 2005 · Replies 4 · Dec 14, 2005

Replies: 4

Views: 11K

Tensor Basics: Understand Tensor or Learn from Websites

Dec 4, 2005 · Replies 3 · Dec 7, 2005

Replies: 3

Views: 2K

What Sets Homeomorphic and Isotopic Knots Apart?

Dec 6, 2005 · Replies 4 · Dec 7, 2005

Replies: 4

Views: 5K

Understanding the Poincare Conjecture: A Layman's Guide

Nov 19, 2005 · Replies 3 · Dec 3, 2005

Replies: 3

Views: 3K

Question about Alexander and Briggs notation

Dec 2, 2005 · Replies 1 · Dec 2, 2005

Replies: 1

Views: 5K

Projective plane as quotient space of a sphere

Nov 22, 2005 · Replies 8 · Nov 28, 2005

Replies: 8

Views: 10K

What are one-forms and why are they sometimes called covectors?

Nov 13, 2005 · Replies 5 · Nov 21, 2005

Replies: 5

Views: 4K

An extension of the concept of a tensor field

Mar 17, 2005 · Replies 2 · Nov 15, 2005

Replies: 2

Views: 3K

Symmetric Matrices and Manifolds Answer Guide

Nov 14, 2005 · Replies 3 · Nov 14, 2005

Replies: 3

Views: 6K

Proving Manifold Problems in R^4: X at a Point a

Nov 14, 2005 · Replies 3 · Nov 14, 2005

Replies: 3

Views: 5K

Is the neighborhood of each point on a surface always open?

Nov 14, 2005 · Replies 1 · Nov 14, 2005

Replies: 1

Views: 2K

One-Form Property: Super-Commutativity vs Anti-Commutativity

Nov 13, 2005 · Replies 2 · Nov 13, 2005

Replies: 2

Views: 3K

Learn Tensor & Topology: Self-Study Resources for Physics B.S. & CAS Fellow

Nov 11, 2005 · Replies 2 · Nov 12, 2005

Replies: 2

Views: 3K

Calculate Exterior Differentials: Step-by-Step Guide

Nov 10, 2005 · Replies 4 · Nov 12, 2005

Replies: 4

Views: 4K

Transform Calc on S^3 to S^2: Maifold Calculus

Nov 4, 2005 · Replies 4 · Nov 10, 2005

Replies: 4

Views: 3K

Fourier transform integral in S^3 by a Hopf fibration to S^2

Nov 3, 2005 · Replies 3 · Nov 6, 2005

Replies: 3

Views: 3K

Why are tangent vectors defined as equivalence classes of paths through a point?

Oct 15, 2005 · Replies 21 · Nov 3, 2005

Replies: 21

Views: 6K

What r the prerequisites for studying diff geo?

Nov 3, 2005 · Replies 2 · Nov 3, 2005

Replies: 2

Views: 3K

How Does Parametric Volume Calculation Work in Four-Dimensional Euclidean Space?

Oct 29, 2005 · Replies 1 · Oct 30, 2005

Replies: 1

Views: 3K

Parallel Transport Around Triangle on Sphere: Angles Excess 180°

Oct 23, 2005 · Replies 4 · Oct 27, 2005

Replies: 4

Views: 3K

How can i define Hook's Law interm of Tensor

Oct 11, 2005 · Replies 5 · Oct 21, 2005

Replies: 5

Views: 11K

Atlas of Manifold: Is it Countable?

Oct 13, 2005 · Replies 2 · Oct 15, 2005

Replies: 2

Views: 5K

How to show something is a tensor.

Oct 12, 2005 · Replies 2 · Oct 12, 2005

Replies: 2

Views: 9K

How to deduce rot and div formulas under spherical or cylinderical coordinat

Oct 4, 2005 · Replies 4 · Oct 10, 2005

Replies: 4

Views: 5K

How Does Tensor Algebra Apply in Quantum Field Theory?

Oct 7, 2005 · Replies 4 · Oct 9, 2005

Replies: 4

Views: 4K

Expanding Subscripts & Putting TeX in Board Posts

Sep 20, 2005 · Replies 7 · Oct 3, 2005

Replies: 7

Views: 4K

Is Projective Geometry the Ultimate Form of Kleinian Geometry?

Sep 20, 2005 · Replies 1 · Sep 20, 2005

Replies: 1

Views: 3K

Good Texts for Independent Study

Aug 10, 2005 · Replies 8 · Sep 9, 2005

Replies: 8

Views: 6K

Understanding Riemann Roch: A Summary of the Classical Proof by Riemann and Roch

Aug 14, 2005 · Replies 14 · Aug 20, 2005

Replies: 14

Views: 6K

Topology Problem 1: Show A is Open in X - Munkres pg 83

Jul 30, 2005 · Replies 6 · Aug 11, 2005

Replies: 6

Views: 4K

Can Mathematical Induction Prove the Finite Difference Formula for Polynomials?

Aug 9, 2005 · Replies 2 · Aug 10, 2005

Replies: 2

Views: 3K

Tensor analysis in curvilinear coordinates

Aug 2, 2005 · Replies 2 · Aug 3, 2005

Replies: 2

Views: 6K

Deriving the Implicit Equation of a Rotated Spheroid

Jul 31, 2005 · Replies 4 · Aug 2, 2005

Replies: 4

Views: 4K

Plane with four corner 3-D (x,y,z)

Jul 25, 2005 · Replies 2 · Jul 26, 2005

Replies: 2

Views: 8K

Difference Between Matrices & Tensors: Explained

Jul 6, 2005 · Replies 10 · Jul 21, 2005

Replies: 10

Views: 5K

Rotate Spheroid: Find Projection Outline on xy-Plane

Jul 15, 2005 · Replies 11 · Jul 20, 2005

Replies: 11

Views: 4K

Orientable Manifold with Boundary

Jul 5, 2005 · Replies 27 · Jul 20, 2005

Replies: 27

Views: 9K

Solving Linear Interpolation for 3-D Triangle Edges

Jul 11, 2005 · Replies 1 · Jul 18, 2005

Replies: 1

Views: 4K

Topology Problem: Homeomorphism in R^n Subspaces

Jul 6, 2005 · Replies 23 · Jul 17, 2005

Replies: 23

Views: 5K

Implementing a 3-Sphere Model for Molecular Dynamics Simulations

Jul 7, 2005 · Replies 2 · Jul 15, 2005

Replies: 2

Views: 5K

Funny definition of dimension of a topological space

Jul 10, 2005 · Replies 11 · Jul 15, 2005

Replies: 11

Views: 5K

Tensor Product of Inner Product Spaces V & W

Jul 7, 2005 · Replies 10 · Jul 14, 2005

Replies: 10

Views: 4K

Flat torus embedding in euclidean space?

Jul 1, 2005 · Replies 13 · Jul 13, 2005

Replies: 13

Views: 7K

Are There Unique Surfaces in R^4 but Not in R^3?

May 13, 2005 · Replies 27 · Jul 2, 2005

Replies: 27

Views: 6K

Proving E_{ij,k} as a Tensor: A Comprehensive Explanation

Jun 25, 2005 · Replies 5 · Jun 27, 2005

Replies: 5

Views: 3K

How Does Covariant Derivative Relate to Curvature in Nonabelian Gauge Fields?

Jun 3, 2005 · Replies 5 · Jun 26, 2005

Replies: 5

Views: 4K

Question regarding tensors derive acceleration in polar form

Jun 21, 2005 · Replies 2 · Jun 21, 2005

Replies: 2

Views: 5K

Got the theorem, having trouble with the proof

Jun 12, 2005 · Replies 5 · Jun 13, 2005

Replies: 5

Views: 3K

How to satisfy Laplace's equation ?

Jun 2, 2005 · Replies 6 · Jun 2, 2005

Replies: 6

Views: 9K

Engineer becomes physicist? help me.

May 10, 2005 · Replies 2 · May 20, 2005

Replies: 2

Views: 4K

Proving Determinant Function Open Mapping: nxn Matrix

May 7, 2005 · Replies 52 · May 16, 2005

2

Replies: 52

Views: 10K

Formula for non-linear differential forms

May 14, 2005 · Replies 14 · May 16, 2005

Replies: 14

Views: 3K

Smooth Surface Transformation for Gents: From One Metric to Another

May 16, 2005 · Replies 3 · May 16, 2005

Replies: 3

Views: 3K

Differential Forms: What You'll Learn in Differential Geometry

May 7, 2005 · Replies 8 · May 9, 2005

Replies: 8

Views: 6K

Learning Lie Groups and Manifolds: An Easy Guide with Examples

Apr 18, 2005 · Replies 14 · May 9, 2005

Replies: 14

Views: 5K

Is the Given 4D Manifold Closed?

May 2, 2005 · Replies 17 · May 7, 2005

Replies: 17

Views: 5K

What is a tensor and why is it useful?

May 2, 2005 · Replies 3 · May 4, 2005

Replies: 3

Views: 6K

Is the Angle A'ô'B' Always 90 Degrees in a Special Case?

Apr 30, 2005 · Replies 2 · May 2, 2005

Replies: 2

Views: 3K

The curmufrence and the volume of a sphere

Apr 24, 2005 · Replies 2 · May 1, 2005

Replies: 2

Views: 3K

Quick question on Einstein Notation

Apr 27, 2005 · Replies 6 · Apr 28, 2005

Replies: 6

Views: 5K

How Does Latitude Affect the Compass Angle of Sunrise?

Apr 18, 2005 · Replies 2 · Apr 26, 2005

Replies: 2

Views: 4K

Hodge Duals and the Interior Product

Apr 24, 2005 · Replies 20 · Apr 26, 2005

Replies: 20

Views: 11K

Changing coordinates mean changing one set of local coordinates

Apr 25, 2005 · Replies 2 · Apr 26, 2005

Replies: 2

Views: 3K

Extension of Thurston's Geometrization Conjecture to four dimensions?

Apr 25, 2005 · Replies 2 · Apr 26, 2005

Replies: 2

Views: 5K

Using surgeries to construct 4-manifolds of arbitrary topology

Apr 17, 2005 · Replies 2 · Apr 21, 2005

Replies: 2

Views: 3K

How Do Cartesian Components Transform into Cylindrical Coordinates?

Mar 28, 2005 · Replies 5 · Apr 16, 2005

Replies: 5

Views: 4K

Question on the properties of a manifold

Apr 8, 2005 · Replies 2 · Apr 15, 2005

Replies: 2

Views: 3K

What is the Vectorfield X(f) for a Function f(x,y,z)?

Apr 3, 2005 · Replies 2 · Apr 10, 2005

Replies: 2

Views: 2K

Solving Curvature Math Problems with Christoffel Symbols

Mar 19, 2005 · Replies 8 · Apr 6, 2005

Replies: 8

Views: 4K

What is a Tensor? Explained in Simple Terms

Mar 19, 2005 · Replies 13 · Apr 5, 2005

Replies: 13

Views: 12K

Extrinsic and Intrinsic Curvature

Mar 17, 2005 · Replies 8 · Mar 27, 2005

Replies: 8

Views: 12K

Writing tensors in a different way?

Mar 3, 2005 · Replies 22 · Mar 19, 2005

Replies: 22

Views: 6K

Proof That An Infinite Dimensional Universe May Not Exist

Mar 7, 2005 · Replies 4 · Mar 17, 2005

Replies: 4

Views: 3K

Is the Definition of a Topological Space Paradoxical?

Feb 26, 2004 · Replies 33 · Mar 9, 2005

2

Replies: 33

Views: 9K

Cross product in higher dimensions?

Mar 5, 2005 · Replies 4 · Mar 6, 2005

Replies: 4

Views: 12K

Manifold Question: Tensor Analysis for Beginners

Mar 2, 2005 · Replies 8 · Mar 3, 2005

Replies: 8

Views: 3K

Can Unbounded 3D Space Truly Exist?

Feb 24, 2005 · Replies 6 · Feb 26, 2005

Replies: 6

Views: 5K

What do topologically stable maps mean?

Feb 7, 2005 · Replies 40 · Feb 23, 2005

2

Replies: 40

Views: 9K

Can Stereographic Projection from Unit Sphere to Plane be Proven as Injective?

Feb 6, 2005 · Replies 2 · Feb 14, 2005

Replies: 2

Views: 4K

Tensors & Differential Geometry - What are lie groups?

Jan 20, 2005 · Replies 9 · Feb 6, 2005

Replies: 9

Views: 5K

Rank 2 covariant tensors and dimesionality

Feb 4, 2005 · Replies 2 · Feb 4, 2005

Replies: 2

Views: 4K

Looking for The Heat Equation Shrinking Convex Plane Curves by M.A. Grayson?

Nov 6, 2004 · Replies 2 · Jan 29, 2005

Replies: 2

Views: 3K

Spinor Decomposition of a tensor

Jan 19, 2005 · Replies 3 · Jan 28, 2005

Replies: 3

Views: 4K

The covariant derivative of a contravariant vector

Jan 21, 2005 · Replies 4 · Jan 24, 2005

Replies: 4

Views: 7K

Calculating Equation of Evolute for Catenary Curve

Jan 16, 2005 · Replies 2 · Jan 21, 2005

Replies: 2

Views: 5K

Differential Equations diameter of a spiral

Jan 2, 2005 · Replies 2 · Jan 2, 2005

Replies: 2

Views: 5K

Closure of an open ball and separable space?

Nov 25, 2004 · Replies 6 · Dec 29, 2004

Replies: 6

Views: 7K

Spherical geometry, some simple things

Dec 23, 2004 · Replies 3 · Dec 26, 2004

Replies: 3

Views: 6K

Solutions in differential forms

Nov 7, 2004 · Replies 4 · Dec 15, 2004

Replies: 4

Views: 5K

Why Doesn't Linearity of Integrals Apply to Differential Forms?

Nov 28, 2004 · Replies 2 · Dec 6, 2004

Replies: 2

Views: 3K

What is a Tensor? Definition & Applications

Aug 7, 2004 · Replies 68 · Nov 30, 2004

3

Replies: 68

Views: 19K

Which Textbook for Studying Homotopy is Best for Beginners?

Nov 27, 2004 · Replies 3 · Nov 29, 2004

Replies: 3

Views: 3K

About the basics of Poisson bracket

Nov 20, 2004 · Replies 3 · Nov 22, 2004

Replies: 3

Views: 5K

Corses on vector and principale bundles and spinorielle geometry

Nov 3, 2004 · Replies 3 · Nov 13, 2004

Replies: 3

Views: 3K

Algebraic Geometry: Proofs, Homeomorphism & Compactness

Sep 28, 2004 · Replies 8 · Nov 10, 2004

Replies: 8

Views: 4K

Differential Geometry And Difference Geometry?

Oct 29, 2004 · Replies 2 · Nov 7, 2004

Replies: 2

Views: 7K

I need to know how can i solve the following

Oct 26, 2004 · Replies 2 · Nov 3, 2004

Replies: 2

Views: 3K

Calculating Volume with Double Integrals: Finding Limits for Enclosed Space

Oct 30, 2004 · Replies 11 · Nov 1, 2004

Replies: 11

Views: 5K

Differential Geometry

Welcome to the Differential Geometry forum!

Differential geometry is a branch of mathematics that combines principles from calculus and geometry to study the properties of curves and surfaces in space. It focuses on understanding how objects curve and bend, incorporating the concept of differentiability.

Differential geometry utilizes tools from calculus, such as derivatives and integrals, to analyze geometric structures and investigate topics like curvature, torsion, and metrics. This field has applications in physics, particularly in the study of general relativity, and plays a crucial role in areas such as computer graphics, where understanding the geometry of surfaces is essential.

Differential geometry provides a powerful framework for describing and analyzing the shapes and structures found in both mathematical abstractions and the physical world.

Top