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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 Extension of Thurston's Geometrization Conjecture to four dimensions?

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

Replies: 2

Graduate How do scientists make sophisticated calculations in general relativity?

Starship
Apr 23, 2005 · Replies 4 · Apr 23, 2005

Replies: 4

Undergrad Pi and Curved Spaces - Is it Constant?

DaveC426913
Apr 21, 2005 · Replies 14 · Apr 22, 2005

Replies: 14

Graduate Using surgeries to construct 4-manifolds of arbitrary topology

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

Replies: 2

Graduate Understanding S^2 as the Quotient of SO(3) and SO(2)

Lonewolf
Apr 20, 2005 · Replies 2 · Apr 20, 2005

Replies: 2

Graduate How Do Cartesian Components Transform into Cylindrical Coordinates?

od7
Mar 28, 2005 · Replies 5 · Apr 16, 2005

Replies: 5

Graduate Question on the properties of a manifold

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

Replies: 2

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

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

Replies: 2

Graduate Solving Curvature Math Problems with Christoffel Symbols

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

Replies: 8

Undergrad What is a Tensor? Explained in Simple Terms

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

Replies: 13

Graduate Proving Orthogonality of Planes and Lines in 3D Geometry

gnome
Mar 27, 2005 · Replies 32 · Mar 30, 2005

2

Replies: 32

Graduate Extrinsic and Intrinsic Curvature

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

Replies: 8

Graduate Writing tensors in a different way?

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

Replies: 22

Graduate Proof That An Infinite Dimensional Universe May Not Exist

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

Replies: 4

Graduate How to Find Functions for Constant Arc Length with Varying Amplitude and Period?

JonF
Mar 17, 2005 · Replies 3 · Mar 17, 2005

Replies: 3

Graduate Moments of Inertia for a right circular solid cone of mass

Claire84
Mar 11, 2005 · Replies 4 · Mar 12, 2005

Replies: 4

Graduate Is the Definition of a Topological Space Paradoxical?

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

2

Replies: 33

Graduate Cross product in higher dimensions?

waht
Mar 5, 2005 · Replies 4 · Mar 6, 2005

Replies: 4

Graduate Manifold Question: Tensor Analysis for Beginners

waht
Mar 2, 2005 · Replies 8 · Mar 3, 2005

Replies: 8

Graduate How many lines can intersect four lines in space?

mathwonk
Feb 10, 2005 · Replies 26 · Mar 2, 2005

Replies: 26

Graduate Can Unbounded 3D Space Truly Exist?

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

Replies: 6

High School Why Don't Surface Area & Volume Ratios of Spheres Match?

vikvon
Feb 24, 2005 · Replies 2 · Feb 24, 2005

Replies: 2

Graduate What do topologically stable maps mean?

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

2

Replies: 40

Graduate Proving Triangle Area of Curve x^2-2y^2=4 Constant

Nima
Feb 14, 2005 · Replies 8 · Feb 14, 2005

Replies: 8

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

T-O7
Feb 6, 2005 · Replies 2 · Feb 14, 2005

Replies: 2

Undergrad Interior angles of a triangle on a spherical surface

Reshma
Feb 9, 2005 · Replies 3 · Feb 10, 2005

Replies: 3

Graduate Tensors & Differential Geometry - What are lie groups?

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

Replies: 9

Graduate Rank 2 covariant tensors and dimesionality

SIlasX
Feb 4, 2005 · Replies 2 · Feb 4, 2005

Replies: 2

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

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

Replies: 2

Graduate Spinor Decomposition of a tensor

njoshi3
Jan 19, 2005 · Replies 3 · Jan 28, 2005

Replies: 3

Graduate The covariant derivative of a contravariant vector

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

Replies: 4

Graduate Calculating Equation of Evolute for Catenary Curve

T-O7
Jan 16, 2005 · Replies 2 · Jan 21, 2005

Replies: 2

Graduate Understanding Differential Geometry in Thermodynamics

vincentchan
Jan 8, 2005 · Replies 12 · Jan 9, 2005

Replies: 12

Undergrad Differential Equations diameter of a spiral

Goo_Gal1
Jan 2, 2005 · Replies 2 · Jan 2, 2005

Replies: 2

Graduate Closure of an open ball and separable space?

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

Replies: 6

Graduate Spherical geometry, some simple things

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

Replies: 3

High School Unravelling Surface Area of a Dome

DaveC426913
Dec 25, 2004 · Replies 2 · Dec 25, 2004

Replies: 2

Graduate Solutions in differential forms

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

Replies: 4

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

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

Replies: 2

Undergrad How Do You Solve Sphere Inscription and Shadow Length Problems?

Kobrakai
Dec 1, 2004 · Replies 2 · Dec 1, 2004

Replies: 2

Undergrad What is a Tensor? Definition & Applications

abercrombiems02
Aug 7, 2004 · Replies 68 · Nov 30, 2004

3

Replies: 68

Graduate Which Textbook for Studying Homotopy is Best for Beginners?

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

Replies: 3

Undergrad What is the formula for finding the surface area of an inclined cone?

Aphex_Twin
Nov 23, 2004 · Replies 3 · Nov 24, 2004

Replies: 3

Graduate About the basics of Poisson bracket

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

Replies: 3

Undergrad Finding Cartesian Equations for Intersecting Planes and a Line

Physics is Phun
Nov 15, 2004 · Replies 5 · Nov 17, 2004

Replies: 5

Graduate Corses on vector and principale bundles and spinorielle geometry

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

Replies: 3

Graduate Algebraic Geometry: Proofs, Homeomorphism & Compactness

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

Replies: 8

Graduate Differential Geometry And Difference Geometry?

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

Replies: 2

Undergrad I need to know how can i solve the following

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

Replies: 2

Undergrad Calculating Volume with Double Integrals: Finding Limits for Enclosed Space

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

Replies: 11

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

vladimir69
Oct 16, 2004 · Replies 18 · Oct 31, 2004

Replies: 18

Graduate Most efficient backgrounder on differential geometry ?

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

Replies: 3

Graduate Visualization of contangent vector?

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

Replies: 10

High School Sum of interior angle is NOT 180, or is 0 degree?

furtivefelon
Oct 29, 2004 · Replies 14 · Oct 30, 2004

Replies: 14

Graduate Non-degenerate Poisson bracket and even-dimensional manifold

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

Replies: 2

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

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

Replies: 4

Graduate Tagent vector and vector field difference

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

Replies: 6

Graduate Understanding the Topology of Klein Bottles and Mobius Strips

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

Replies: 4

Graduate Showing scalars are unchanged by rotation

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

Replies: 2

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

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

Replies: 5

Graduate Distance in hyperbolic geometry

gravenewworld
Oct 5, 2004 · Replies 2 · Oct 5, 2004

Replies: 2

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

Clausius2
Sep 28, 2004 · Replies 1 · Oct 5, 2004

Replies: 1

Graduate Volume of a parallelepiped's sign

quasar987
Oct 3, 2004 · Replies 3 · Oct 4, 2004

Replies: 3

Undergrad Tensors & Manifolds: Best Intro Book for Beginners

galois427
Aug 13, 2004 · Replies 18 · Sep 24, 2004

Replies: 18

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

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

Replies: 2

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

Dr-NiKoN
Sep 13, 2004 · Replies 2 · Sep 20, 2004

Replies: 2

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

Mike2
Jun 3, 2004 · Replies 3 · Sep 18, 2004

Replies: 3

Graduate How Do Lie Groups Influence Physics and Background Independence?

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

Replies: 14

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

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

Replies: 7

Graduate Directionality in Stokes Theorem for Volumes

K.J.Healey
Sep 9, 2004 · Replies 2 · Sep 16, 2004

Replies: 2

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

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

Replies: 5

Graduate What is the Significance of Diffeomorphism Invariance in Physics?

Mike2
Aug 12, 2004 · Replies 7 · Sep 16, 2004

Replies: 7

Graduate Is learning Tensors necessary for understanding Special Relativity?

Severian596
Mar 16, 2004 · Replies 17 · Sep 14, 2004

Replies: 17

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

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

Replies: 20

Graduate Understanding Intrinsic and Extrinsic Curvature: An Intuitive Explanation

Gza
Jun 9, 2004 · Replies 6 · Sep 9, 2004

Replies: 6

Undergrad So what is the relationship between curves and circles?

Mattius_
Sep 4, 2004 · Replies 3 · Sep 5, 2004

Replies: 3

Graduate Unlink Tori with Continuous Deformations: Topology & Free Software

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

Replies: 2

Graduate Finding Total Area of Intersecting Planes

nash_81
Aug 12, 2004 · Replies 5 · Aug 16, 2004

Replies: 5

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

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

Replies: 2

Graduate How can I apply tensor to reality?

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

Replies: 3

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

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

Replies: 20

Graduate What Makes a Vector Different from Other Mathematical Objects?

Mike2
Feb 26, 2004 · Replies 7 · Aug 10, 2004

Replies: 7

Graduate Hodge numbers of 2n-dimensional torus

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

Replies: 2

Graduate Tensor Product of Covariant and Contravariant Vectors

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

Replies: 5

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

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

Replies: 5

Graduate Can Planar Surfaces Form Knots in Four Dimensions?

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

Replies: 3

Undergrad Solving Tangent Plane and Perpendicular Plane at (1,1,1)

brads
Jul 17, 2004 · Replies 4 · Jul 17, 2004

Replies: 4

Graduate Covariance of Differential Operators in Special Relativity

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

Replies: 2

Undergrad Cube Question In Space Geometry

xenogizmo
Jul 13, 2004 · Replies 2 · Jul 14, 2004

Replies: 2

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

alexh110
Jan 12, 2004 · Replies 3 · Jul 14, 2004

Replies: 3

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

Loren Booda
Jul 7, 2004 · Replies 1 · Jul 7, 2004

Replies: 1

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

lost1
Jul 3, 2004 · Replies 1 · Jul 3, 2004

Replies: 1

Undergrad Parallel lines and space curvature

wildo69
Jun 18, 2004 · Replies 5 · Jun 28, 2004

Replies: 5

Graduate Tensors may be considered a special class

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

Replies: 5

Undergrad What are the uses and properties of a Surface Patch?

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

Replies: 2

Graduate Some basic problems in Riemannian Geometry

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

Replies: 17

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

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

Replies: 2

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

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

Replies: 2

Graduate Proofs of Equations Involving Metric Tensors and Christoffel Symbols

Jinroh
Jun 5, 2004 · Replies 3 · Jun 5, 2004

Replies: 3

Undergrad Tangent/normal/area for this Circle

DavioSenBoo
Jun 3, 2004 · Replies 2 · Jun 3, 2004

Replies: 2

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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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