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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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Graduate Which Textbook for Studying Homotopy is Best for Beginners?

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

Replies: 3

Views: 3K

Graduate About the basics of Poisson bracket

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

Replies: 3

Views: 5K

Graduate Corses on vector and principale bundles and spinorielle geometry

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

Replies: 3

Views: 3K

Graduate Algebraic Geometry: Proofs, Homeomorphism & Compactness

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

Replies: 8

Views: 4K

Graduate Differential Geometry And Difference Geometry?

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

Replies: 2

Views: 7K

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

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

Replies: 18

Views: 10K

Graduate Most efficient backgrounder on differential geometry ?

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

Replies: 3

Views: 3K

Graduate Visualization of contangent vector?

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

Replies: 10

Views: 6K

Graduate Non-degenerate Poisson bracket and even-dimensional manifold

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

Replies: 2

Views: 4K

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

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

Replies: 4

Views: 5K

Graduate Tagent vector and vector field difference

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

Replies: 6

Views: 7K

Graduate Understanding the Topology of Klein Bottles and Mobius Strips

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

Replies: 4

Views: 6K

Graduate Showing scalars are unchanged by rotation

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

Replies: 2

Views: 3K

Graduate 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

Graduate Distance in hyperbolic geometry

Oct 5, 2004 · Replies 2 · Oct 5, 2004

Replies: 2

Views: 4K

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

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

Replies: 1

Views: 3K

Graduate Volume of a parallelepiped's sign

Oct 3, 2004 · Replies 3 · Oct 4, 2004

Replies: 3

Views: 3K

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

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

Replies: 2

Views: 3K

Graduate 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

Graduate How Do Lie Groups Influence Physics and Background Independence?

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

Replies: 14

Views: 5K

Graduate 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

Graduate Directionality in Stokes Theorem for Volumes

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

Replies: 2

Views: 3K

Graduate What Are the Practical Applications of Differential Geometry Beyond Mathematics?

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

Replies: 5

Views: 4K

Graduate What is the Significance of Diffeomorphism Invariance in Physics?

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

Replies: 7

Views: 6K

Graduate Is learning Tensors necessary for understanding Special Relativity?

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

Replies: 17

Views: 6K

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

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

Replies: 20

Views: 20K

Graduate Understanding Intrinsic and Extrinsic Curvature: An Intuitive Explanation

Jun 9, 2004 · Replies 6 · Sep 9, 2004

Replies: 6

Views: 7K

Graduate Unlink Tori with Continuous Deformations: Topology & Free Software

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

Replies: 2

Views: 4K

Graduate Finding Total Area of Intersecting Planes

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

Replies: 5

Views: 4K

Graduate How can I apply tensor to reality?

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

Replies: 3

Views: 4K

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

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

Replies: 20

Views: 15K

Graduate What Makes a Vector Different from Other Mathematical Objects?

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

Replies: 7

Views: 5K

Graduate Hodge numbers of 2n-dimensional torus

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

Replies: 2

Views: 7K

Graduate Tensor Product of Covariant and Contravariant Vectors

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

Replies: 5

Views: 6K

Graduate What Are the Best Books for Understanding Manifolds and Tensors?

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

Replies: 5

Views: 6K

Graduate Can Planar Surfaces Form Knots in Four Dimensions?

Jul 19, 2004 · Replies 3 · Jul 21, 2004

Replies: 3

Views: 3K

Graduate Covariance of Differential Operators in Special Relativity

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

Replies: 2

Views: 4K

Graduate What Are the Key Groups in Gravity and Quantum Gravity?

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

Replies: 3

Views: 4K

Graduate How Does Curvature Vary in Non-Euclidean Triangle Manifolds?

Jul 7, 2004 · Replies 1 · Jul 7, 2004

Replies: 1

Views: 4K

Graduate Finding Tangent Vectors for Unit Normal (nx=ny=nz)

Jul 3, 2004 · Replies 1 · Jul 3, 2004

Replies: 1

Views: 3K

Graduate Tensors may be considered a special class

May 14, 2004 · Replies 5 · Jun 21, 2004

Replies: 5

Views: 5K

Graduate Some basic problems in Riemannian Geometry

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

Replies: 17

Views: 7K

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

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

Replies: 2

Views: 5K

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

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

Replies: 2

Views: 5K

Graduate Proofs of Equations Involving Metric Tensors and Christoffel Symbols

Jun 5, 2004 · Replies 3 · Jun 5, 2004

Replies: 3

Views: 12K

Graduate Riemannian Geometry: What is It?

Apr 25, 2004 · Replies 12 · May 30, 2004

Replies: 12

Views: 3K

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

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

Replies: 3

Views: 3K

Graduate How Do You Determine the Minimal Distance to a Circle in 3D Space?

May 13, 2004 · Replies 7 · May 13, 2004

Replies: 7

Views: 4K

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

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

Replies: 2

Views: 6K

Graduate How to Calculate Structure Constants for Reparametrized Rotation Group?

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

Replies: 1

Views: 3K

Graduate Expanding manifold with constant boundary

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

Replies: 8

Views: 4K

Graduate If curvature were an exact differential

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

Replies: 7

Views: 4K

Graduate Lie transport vs. parallel transport

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

Replies: 10

Views: 12K

Graduate Proving Q = gradP + Sr for Splitting Vector Field B

Mar 24, 2004 · Replies 6 · Mar 25, 2004

Replies: 6

Views: 2K

Graduate Quick Introduction to Tensor Analysis

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

Replies: 3

Views: 13K

Graduate Coordinate Transforms: Idiot's Guide & Rules of Thumb

Mar 23, 2004 · Replies 1 · Mar 23, 2004

Replies: 1

Views: 2K

Graduate Decomposition of a Divergenceless Vector Field

Mar 16, 2004 · Replies 1 · Mar 17, 2004

Replies: 1

Views: 3K

Graduate 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

Graduate Hausdorff topological space M of dimension m

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

Replies: 2

Views: 5K

Graduate Request for help and/or comments

Mar 2, 2004 · Replies 2 · Mar 4, 2004

Replies: 2

Views: 4K

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

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

Replies: 5

Views: 5K

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

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

Replies: 12

Views: 5K

Graduate 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

Graduate Theorem between Curvature and submanifolds

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

Replies: 13

Views: 4K

Graduate Definition of a vector using transformations

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

Replies: 4

Views: 7K

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

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

Replies: 4

Views: 6K

Graduate Can You Simplify Inertia Tensor Calculations for 3D Objects?

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

Replies: 2

Views: 15K

Graduate Metrics and coordinate transforms

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

Replies: 14

Views: 6K

Graduate Drawing Curve in R2 Space: ds2=y2dx2+dy2

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

Replies: 2

Views: 5K

Graduate Pronouncing Synge's Theorem: Connecting Curvature and Genus

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

Replies: 18

Views: 8K

Graduate Proposed Resource Sticky for Quantum Differential Geometry

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

Replies: 2

Views: 5K

Graduate Basic tools for quantized differential geometry

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

Replies: 2

Views: 6K

Graduate Comments on Toy Principle Bundle

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

Replies: 2

Views: 4K

Graduate Building a Toy Principle Bundle: Visualizing Connections on Manifolds

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

Replies: 2

Views: 6K

Graduate Can Singularities Be Modeled as a Conventional Field?

Sep 9, 2003 · Replies 3 · Sep 11, 2003

Replies: 3

Views: 3K

Graduate Fresh start at a (Loop) Quantum Gravity thread

Aug 3, 2003 · Replies 12 · Aug 25, 2003

Replies: 12

Views: 4K

Graduate Principal G-bundle and bundle of bases (footnote)

Aug 11, 2003 · Replies 2 · Aug 13, 2003

Replies: 2

Views: 5K

Graduate Development of Loop Quantum Gravity

Aug 8, 2003 · Replies 22 · Aug 12, 2003

Replies: 22

Views: 7K

Graduate Who's better, Baez or Rovelli? (at explaining GR)

Aug 7, 2003 · Replies 4 · Aug 7, 2003

Replies: 4

Views: 3K

Graduate One half of LQG's proposed math framework topic

Jul 21, 2003 · Replies 7 · Jul 26, 2003

Replies: 7

Views: 3K

Graduate What is the best font for displaying mathematical symbols?

Jul 10, 2003 · Replies 2 · Jul 11, 2003

Replies: 2

Views: 3K

Graduate Thetas, tets, sixjays and such

Jul 8, 2003 · Replies 4 · Jul 8, 2003

Replies: 4

Views: 3K

Graduate Unveiling the Connection: Rotation Groups & Hyperspheres

May 3, 2003 · Replies 2 · Jun 11, 2003

Replies: 2

Views: 3K

Graduate Smallest Dimension Hypersphere & Constructing Non-Geodesic Line

May 3, 2003 · Replies 5 · May 10, 2003

Replies: 5

Views: 3K

Graduate How Are Surface Curvatures Derived from Implicit and Parametric Forms?

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

Replies: 16

Views: 5K

Graduate Rotation and increasing radius

Apr 21, 2003 · Replies 21 · Apr 28, 2003

Replies: 21

Views: 7K

Graduate Understanding Moments of Inertia & Tensors

Apr 16, 2003 · Replies 14 · Apr 21, 2003

Replies: 14

Views: 4K

Graduate N-dimensional geometric partitioning

Mar 21, 2003 · Replies 10 · Mar 22, 2003

Replies: 10

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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