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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 Questions on Contracting (1,1) Tensors & (2,0) Tensors

Ratzinger
Jan 20, 2006 · Replies 16 · Jan 24, 2006

Replies: 16

Undergrad Euclidean and Non Euclidean Space?

sepulshan
Jan 22, 2006 · Replies 1 · Jan 22, 2006

Replies: 1

Graduate Worked Problems in Modern Differential Geometry

rick1138
Jan 12, 2006 · Replies 2 · Jan 18, 2006

Replies: 2

Graduate How Does Variation in the Metric Determinant Depend on Its Inverse?

Themetricsystem
Jan 15, 2006 · Replies 1 · Jan 16, 2006

Replies: 1

Undergrad Equation of a Line in three space question

thomasrules
Jan 13, 2006 · Replies 9 · Jan 14, 2006

Replies: 9

Graduate Definition of a smooth manifold.

vanesch
Dec 13, 2005 · Replies 27 · Jan 9, 2006

Replies: 27

Graduate Understanding the Connection between Physics Tensors and Algebra Tensoring

homology
Jan 5, 2006 · Replies 7 · Jan 8, 2006

Replies: 7

Graduate Qestion: Vector field and (n-1)-form representation of current density

mma
Jan 4, 2006 · Replies 6 · Jan 4, 2006

Replies: 6

Graduate Unifying Curvatures with Riemann Tensor

bchui
Dec 30, 2005 · Replies 2 · Dec 31, 2005

Replies: 2

Graduate Two quick questions on subspaces (intro to tensor calc)

Ed Quanta
Dec 25, 2005 · Replies 1 · Dec 26, 2005

Replies: 1

Graduate Can a Möbius Strip be embedded in R3 with zero Gaussian curvature?

Ogai
Dec 21, 2005 · Replies 8 · Dec 23, 2005

Replies: 8

Graduate The Geometric Heat Equation-WTF?

the.bone
Dec 1, 2005 · Replies 3 · Dec 22, 2005

Replies: 3

Graduate Geometry - Stereographic projection

Pearce_09
Dec 19, 2005 · Replies 2 · Dec 21, 2005

Replies: 2

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

rick1138
Dec 15, 2005 · Replies 2 · Dec 19, 2005

Replies: 2

Graduate Physics & Topology: Research, Books & Articles

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

Replies: 4

Undergrad Tensor Basics: Understand Tensor or Learn from Websites

pastadude
Dec 4, 2005 · Replies 3 · Dec 7, 2005

Replies: 3

Graduate What Sets Homeomorphic and Isotopic Knots Apart?

ComputerGeek
Dec 6, 2005 · Replies 4 · Dec 7, 2005

Replies: 4

Graduate Understanding the Poincare Conjecture: A Layman's Guide

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

Replies: 3

Graduate Question about Alexander and Briggs notation

ComputerGeek
Dec 2, 2005 · Replies 1 · Dec 2, 2005

Replies: 1

Graduate Projective plane as quotient space of a sphere

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

Replies: 8

Graduate Deriving the Value of the Sum in {_\lim {i} \rightarrow 0}

Werg22
Nov 15, 2005 · Replies 5 · Nov 26, 2005

Replies: 5

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

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

Replies: 5

Graduate An extension of the concept of a tensor field

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

Replies: 2

Graduate Symmetric Matrices and Manifolds Answer Guide

'AQF
Nov 14, 2005 · Replies 3 · Nov 14, 2005

Replies: 3

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

'AQF
Nov 14, 2005 · Replies 3 · Nov 14, 2005

Replies: 3

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

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

Replies: 1

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

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

Replies: 2

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

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

Replies: 2

Graduate Calculate Exterior Differentials: Step-by-Step Guide

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

Replies: 4

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

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

Replies: 4

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

htaati
Nov 3, 2005 · Replies 3 · Nov 6, 2005

Replies: 3

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

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

Replies: 21

Undergrad What r the prerequisites for studying diff geo?

pavanakumar
Nov 3, 2005 · Replies 2 · Nov 3, 2005

Replies: 2

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

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

Replies: 1

Graduate Parallel Transport Around Triangle on Sphere: Angles Excess 180°

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

Replies: 4

Graduate How can i define Hook's Law interm of Tensor

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

Replies: 5

Graduate Atlas of Manifold: Is it Countable?

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

Replies: 2

Graduate How to show something is a tensor.

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

Replies: 2

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

Dale12
Oct 4, 2005 · Replies 4 · Oct 10, 2005

Replies: 4

Graduate How Does Tensor Algebra Apply in Quantum Field Theory?

Spinny
Oct 7, 2005 · Replies 4 · Oct 9, 2005

Replies: 4

Graduate Expanding Subscripts & Putting TeX in Board Posts

bigplanet401
Sep 20, 2005 · Replies 7 · Oct 3, 2005

Replies: 7

Graduate Is Projective Geometry the Ultimate Form of Kleinian Geometry?

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

Replies: 1

Graduate How can I find Va given Vo and angle A on a 3D sphere?

Ed
Sep 7, 2005 · Replies 2 · Sep 12, 2005

Replies: 2

Graduate Parametrization of a Moebius Strip

amcavoy
Sep 2, 2005 · Replies 10 · Sep 12, 2005

Replies: 10

Undergrad Good Texts for Independent Study

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

Replies: 8

Graduate Radius of curvature formula derivation

chandran
Sep 4, 2005 · Replies 2 · Sep 4, 2005

Replies: 2

Undergrad Why Is \(\phi\) Defined Differently in Spherical Coordinates?

bomba923
Sep 3, 2005 · Replies 3 · Sep 3, 2005

Replies: 3

Undergrad Find an Equation of Plane Through P (3,3,1) Perpendicular to Planes

Giuseppe
Sep 1, 2005 · Replies 1 · Sep 1, 2005

Replies: 1

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

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

Replies: 14

Graduate Surface Area of an N-Dimensional Sphere

fizixx
Aug 12, 2005 · Replies 9 · Aug 14, 2005

Replies: 9

Undergrad What is the meaning of the term 'surface term'?

Ratzinger
Aug 8, 2005 · Replies 11 · Aug 11, 2005

Replies: 11

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

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

Replies: 6

Graduate Can Mathematical Induction Prove the Finite Difference Formula for Polynomials?

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

Replies: 2

Graduate Can a 'Good Surface' Be Found for Any Continuous Vector Field?

HungryChemist
Aug 10, 2005 · Replies 2 · Aug 10, 2005

Replies: 2

Undergrad How can I solve a 3D coordinate problem involving rotation and a given point?

pimanian
Aug 8, 2005 · Replies 1 · Aug 8, 2005

Replies: 1

Graduate Solve Tangent Equation: Find A, B, & C for Ellipse

kidia
Aug 1, 2005 · Replies 5 · Aug 6, 2005

Replies: 5

Undergrad Tensor analysis in curvilinear coordinates

hbar314
Aug 2, 2005 · Replies 2 · Aug 3, 2005

Replies: 2

Graduate Deriving the Implicit Equation of a Rotated Spheroid

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

Replies: 4

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

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

Replies: 2

Graduate Is an N-Sphere Just a Solid Ball or Something More?

yourdadonapogostick
Jul 24, 2005 · Replies 10 · Jul 25, 2005

Replies: 10

Undergrad Difference Between Matrices & Tensors: Explained

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

Replies: 10

Graduate Rotate Spheroid: Find Projection Outline on xy-Plane

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

Replies: 11

Graduate Orientable Manifold with Boundary

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

Replies: 27

High School Why Doesn't My 2-Sphere Graph Correctly in GraphCalc?

yourdadonapogostick
Jul 18, 2005 · Replies 1 · Jul 18, 2005

Replies: 1

Graduate Solving Linear Interpolation for 3-D Triangle Edges

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

Replies: 1

Graduate Topology Problem: Homeomorphism in R^n Subspaces

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

Replies: 23

Graduate Implementing a 3-Sphere Model for Molecular Dynamics Simulations

quetzalcoatl9
Jul 7, 2005 · Replies 2 · Jul 15, 2005

Replies: 2

Graduate Funny definition of dimension of a topological space

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

Replies: 11

Graduate Tensor Product of Inner Product Spaces V & W

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

Replies: 10

Undergrad Finding Slopes of Warped Plane: A,B,C,D,X

laminatedevildoll
Jul 12, 2005 · Replies 3 · Jul 13, 2005

Replies: 3

Graduate Flat torus embedding in euclidean space?

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

Replies: 13

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

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

Replies: 27

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

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

Replies: 5

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

wac03
Jun 3, 2005 · Replies 5 · Jun 26, 2005

Replies: 5

Graduate Vector parallel to our instantaneous direction of travel

touqra
Jun 22, 2005 · Replies 6 · Jun 23, 2005

Replies: 6

Graduate Question regarding tensors derive acceleration in polar form

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

Replies: 2

Undergrad Find Largest Dropping Circle in Parabola & x^4 Graphs

Saint Medici
Jul 26, 2004 · Replies 5 · Jun 21, 2005

Replies: 5

Graduate Find Center of Sheared Cylinder (x, y, z, θ)

isabella
Jun 14, 2005 · Replies 1 · Jun 14, 2005

Replies: 1

Undergrad Where is the Angle Theta Measured in a Cylinder's Surface Area?

isabella
Jun 13, 2005 · Replies 1 · Jun 14, 2005

Replies: 1

Graduate Got the theorem, having trouble with the proof

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

Replies: 5

Undergrad How to satisfy Laplace's equation ?

hotel
Jun 2, 2005 · Replies 6 · Jun 2, 2005

Replies: 6

Graduate Gradient in cylindrical coordinates

sid_galt
May 26, 2005 · Replies 1 · May 26, 2005

Replies: 1

Graduate Engineer becomes physicist? help me.

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

Replies: 2

Graduate Proving Determinant Function Open Mapping: nxn Matrix

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

2

Replies: 52

Graduate Formula for non-linear differential forms

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

Replies: 14

Graduate Smooth Surface Transformation for Gents: From One Metric to Another

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

Replies: 3

Graduate Finding the Centre of Mass and Toppling Point of a Spinning Top

vic
May 11, 2005 · Replies 4 · May 14, 2005

Replies: 4

Graduate Differential Forms: What You'll Learn in Differential Geometry

quasar987
May 7, 2005 · Replies 8 · May 9, 2005

Replies: 8

Graduate Learning Lie Groups and Manifolds: An Easy Guide with Examples

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

Replies: 14

Graduate Is the Given 4D Manifold Closed?

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

Replies: 17

Undergrad Probably quite simple but i'm stuck

.....
May 5, 2005 · Replies 5 · May 5, 2005

Replies: 5

Undergrad What is a tensor and why is it useful?

relativitydude
May 2, 2005 · Replies 3 · May 4, 2005

Replies: 3

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

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

Replies: 2

High School The curmufrence and the volume of a sphere

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

Replies: 2

Graduate Quick question on Einstein Notation

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

Replies: 6

Undergrad Solving Tangent Equation at Point P: r(t) = (t, t^2, t^3)

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

Replies: 6

Graduate How Does Latitude Affect the Compass Angle of Sunrise?

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

Replies: 2

Graduate Hodge Duals and the Interior Product

Kane O'Donnell
Apr 24, 2005 · Replies 20 · Apr 26, 2005

Replies: 20

Graduate Is a homomorphism sending an element

Lonewolf
Apr 25, 2005 · Replies 5 · Apr 26, 2005

Replies: 5

Graduate Changing coordinates mean changing one set of local coordinates

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

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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