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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.

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Proof that grad V is a (1,1) tensor

Oct 16, 2004 · Replies 18 · Oct 31, 2004

Replies: 18

Views: 10K

Most efficient backgrounder on differential geometry ?

Oct 17, 2004 · Replies 3 · Oct 31, 2004

Replies: 3

Views: 3K

Visualization of contangent vector?

Oct 28, 2004 · Replies 10 · Oct 30, 2004

Replies: 10

Views: 6K

Non-degenerate Poisson bracket and even-dimensional manifold

Oct 17, 2004 · Replies 2 · Oct 28, 2004

Replies: 2

Views: 4K

What Are Quotient Spaces and How Can We Visualize Equivalence Classes?

Oct 24, 2004 · Replies 4 · Oct 26, 2004

Replies: 4

Views: 5K

Tagent vector and vector field difference

Oct 13, 2004 · Replies 6 · Oct 23, 2004

Replies: 6

Views: 7K

Understanding the Topology of Klein Bottles and Mobius Strips

Oct 21, 2004 · Replies 4 · Oct 22, 2004

Replies: 4

Views: 6K

Showing scalars are unchanged by rotation

Oct 10, 2004 · Replies 2 · Oct 22, 2004

Replies: 2

Views: 3K

What is the 2nd Fundamental Form and how does it relate to geometry in 3-space?

Oct 8, 2004 · Replies 5 · Oct 21, 2004

Replies: 5

Views: 4K

How to Cluster Lines in an Elliptic Mesh Generator Using Matlab?

Sep 28, 2004 · Replies 1 · Oct 5, 2004

Replies: 1

Views: 3K

Tensors & Manifolds: Best Intro Book for Beginners

Aug 13, 2004 · Replies 18 · Sep 24, 2004

Replies: 18

Views: 11K

Where Can I Find Master's Level Courses in Differential Geometry?

Sep 16, 2004 · Replies 2 · Sep 23, 2004

Replies: 2

Views: 3K

Understanding Curves: f(x) = sin(x), g(x) = cos(x)

Sep 13, 2004 · Replies 2 · Sep 20, 2004

Replies: 2

Views: 5K

Is the Algebraic Structure of Vector Bundles Truly Just a Module Theory Analogy?

Jun 3, 2004 · Replies 3 · Sep 18, 2004

Replies: 3

Views: 6K

How Do Lie Groups Influence Physics and Background Independence?

Sep 2, 2004 · Replies 14 · Sep 17, 2004

Replies: 14

Views: 5K

How do I prove that d^u(phi) is a contravariant 4-vector?

Sep 11, 2004 · Replies 7 · Sep 16, 2004

Replies: 7

Views: 7K

Directionality in Stokes Theorem for Volumes

Sep 9, 2004 · Replies 2 · Sep 16, 2004

Replies: 2

Views: 3K

What Are the Practical Applications of Differential Geometry Beyond Mathematics?

Aug 15, 2004 · Replies 5 · Sep 16, 2004

Replies: 5

Views: 4K

What is the Significance of Diffeomorphism Invariance in Physics?

Aug 12, 2004 · Replies 7 · Sep 16, 2004

Replies: 7

Views: 6K

Is learning Tensors necessary for understanding Special Relativity?

Mar 16, 2004 · Replies 17 · Sep 14, 2004

Replies: 17

Views: 6K

What is the significance of the Christoffel symbol as a tensor?

Aug 22, 2004 · Replies 20 · Sep 13, 2004

Replies: 20

Views: 20K

Understanding Intrinsic and Extrinsic Curvature: An Intuitive Explanation

Jun 9, 2004 · Replies 6 · Sep 9, 2004

Replies: 6

Views: 7K

Unlink Tori with Continuous Deformations: Topology & Free Software

May 31, 2004 · Replies 2 · Aug 17, 2004

Replies: 2

Views: 4K

Finding Total Area of Intersecting Planes

Aug 12, 2004 · Replies 5 · Aug 16, 2004

Replies: 5

Views: 3K

What are some practical applications of tensors in physics and mathematics?

Aug 8, 2004 · Replies 2 · Aug 15, 2004

Replies: 2

Views: 8K

How can I apply tensor to reality?

Aug 7, 2004 · Replies 3 · Aug 11, 2004

Replies: 3

Views: 4K

What are differential forms and why are they important in physics?

Oct 28, 2003 · Replies 20 · Aug 10, 2004

Replies: 20

Views: 15K

What Makes a Vector Different from Other Mathematical Objects?

Feb 26, 2004 · Replies 7 · Aug 10, 2004

Replies: 7

Views: 5K

Hodge numbers of 2n-dimensional torus

Apr 21, 2004 · Replies 2 · Aug 10, 2004

Replies: 2

Views: 7K

Tensor Product of Covariant and Contravariant Vectors

Apr 17, 2004 · Replies 5 · Aug 10, 2004

Replies: 5

Views: 6K

What Are the Best Books for Understanding Manifolds and Tensors?

Oct 16, 2003 · Replies 5 · Aug 10, 2004

Replies: 5

Views: 6K

Covariance of Differential Operators in Special Relativity

Jul 16, 2004 · Replies 2 · Jul 17, 2004

Replies: 2

Views: 4K

What Are the Key Groups in Gravity and Quantum Gravity?

Jan 12, 2004 · Replies 3 · Jul 14, 2004

Replies: 3

Views: 4K

Parallel lines and space curvature

Jun 18, 2004 · Replies 5 · Jun 28, 2004

Replies: 5

Views: 12K

What are the uses and properties of a Surface Patch?

Jun 7, 2004 · Replies 2 · Jun 14, 2004

Replies: 2

Views: 10K

Some basic problems in Riemannian Geometry

Jun 7, 2004 · Replies 17 · Jun 13, 2004

Replies: 17

Views: 7K

How can we prove the covariant derivation of the Riemann-Christoffel tensor?

Jun 11, 2004 · Replies 2 · Jun 12, 2004

Replies: 2

Views: 5K

Where Can I Find a Proof for the Four Vertex Theorem?

May 29, 2004 · Replies 2 · Jun 6, 2004

Replies: 2

Views: 5K

Proofs of Equations Involving Metric Tensors and Christoffel Symbols

Jun 5, 2004 · Replies 3 · Jun 5, 2004

Replies: 3

Views: 12K

Tangent/normal/area for this Circle

Jun 3, 2004 · Replies 2 · Jun 3, 2004

Replies: 2

Views: 11K

What Are the Best Resources to Learn About Non-Commutative Geometry?

May 25, 2004 · Replies 3 · May 27, 2004

Replies: 3

Views: 3K

How Do You Find a Plane That Contains One Line and Is Parallel to Another?

May 23, 2004 · Replies 6 · May 25, 2004

Replies: 6

Views: 5K

How Can I Improve My Understanding of Twisted Forms in Mathematics?

Apr 10, 2004 · Replies 2 · Apr 29, 2004

Replies: 2

Views: 6K

How to Calculate Structure Constants for Reparametrized Rotation Group?

Apr 18, 2004 · Replies 1 · Apr 25, 2004

Replies: 1

Views: 3K

Expanding manifold with constant boundary

Mar 27, 2004 · Replies 8 · Apr 14, 2004

Replies: 8

Views: 4K

Homogeneous points & coordinates

Apr 12, 2004 · Replies 5 · Apr 13, 2004

Replies: 5

Views: 5K

If curvature were an exact differential

Mar 31, 2004 · Replies 7 · Apr 11, 2004

Replies: 7

Views: 4K

Removing 200 Points on a Plane: Solving the Circular Answer

Mar 31, 2004 · Replies 11 · Apr 3, 2004

Replies: 11

Views: 4K

Lie transport vs. parallel transport

Mar 25, 2004 · Replies 10 · Mar 31, 2004

Replies: 10

Views: 12K

Scalar & Vector Equations: What is the Difference?

Mar 25, 2004 · Replies 3 · Mar 26, 2004

Replies: 3

Views: 22K

Quick Introduction to Tensor Analysis

Mar 17, 2004 · Replies 3 · Mar 24, 2004

Replies: 3

Views: 13K

Which of the following is a metric on S? d^2 or d^(1/2)

Mar 16, 2004 · Replies 2 · Mar 16, 2004

Replies: 2

Views: 5K

Hausdorff topological space M of dimension m

Mar 14, 2004 · Replies 2 · Mar 14, 2004

Replies: 2

Views: 5K

Request for help and/or comments

Mar 2, 2004 · Replies 2 · Mar 4, 2004

Replies: 2

Views: 4K

How Do You Transform a (1,2) Tensor?

Feb 8, 2004 · Replies 5 · Feb 10, 2004

Replies: 5

Views: 5K

4-volume is a rank (0,0) tensor?

Feb 2, 2004 · Replies 12 · Feb 6, 2004

Replies: 12

Views: 5K

Given a general graph on a plane, deform the plane in 3 space

Feb 5, 2004 · Replies 5 · Feb 6, 2004

Replies: 5

Views: 4K

Theorem between Curvature and submanifolds

Jan 7, 2004 · Replies 13 · Feb 1, 2004

Replies: 13

Views: 4K

Definition of a vector using transformations

Jan 26, 2004 · Replies 4 · Jan 26, 2004

Replies: 4

Views: 7K

Understanding Geodesic Deviation: Solving for Equations (7) to (8)

Jan 24, 2004 · Replies 4 · Jan 25, 2004

Replies: 4

Views: 6K

Analytical Geometry & Linear Algebra at HS

Jan 21, 2004 · Replies 2 · Jan 22, 2004

Replies: 2

Views: 4K

Difference between Plain & Solid Geometry

Jan 10, 2004 · Replies 2 · Jan 17, 2004

Replies: 2

Views: 12K

Can You Simplify Inertia Tensor Calculations for 3D Objects?

Nov 25, 2003 · Replies 2 · Dec 6, 2003

Replies: 2

Views: 15K

Metrics and coordinate transforms

Nov 23, 2003 · Replies 14 · Nov 25, 2003

Replies: 14

Views: 6K

Drawing Curve in R2 Space: ds2=y2dx2+dy2

Nov 3, 2003 · Replies 2 · Nov 21, 2003

Replies: 2

Views: 5K

Pronouncing Synge's Theorem: Connecting Curvature and Genus

Nov 17, 2003 · Replies 18 · Nov 20, 2003

Replies: 18

Views: 8K

The Euler 9 Point Circle: Solving the Mystery of its Triangle Compatibility

Nov 19, 2003 · Replies 2 · Nov 19, 2003

Replies: 2

Views: 7K

Proposed Resource Sticky for Quantum Differential Geometry

Nov 17, 2003 · Replies 2 · Nov 17, 2003

Replies: 2

Views: 5K

Basic tools for quantized differential geometry

Oct 22, 2003 · Replies 2 · Oct 30, 2003

Replies: 2

Views: 6K

Comments on Toy Principle Bundle

Oct 26, 2003 · Replies 2 · Oct 26, 2003

Replies: 2

Views: 4K

Building a Toy Principle Bundle: Visualizing Connections on Manifolds

Oct 26, 2003 · Replies 2 · Oct 26, 2003

Replies: 2

Views: 6K

Differential geometry and tensor calculus

Oct 5, 2003 · Replies 6 · Oct 13, 2003

Replies: 6

Views: 19K

How Are Surface Curvatures Derived from Implicit and Parametric Forms?

Apr 28, 2003 · Replies 16 · May 9, 2003

Replies: 16

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.

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