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.

Threads

Graduate What is the second fundamental form?

  • the.bone
  • · Replies 5 ·
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5

Graduate Contracting (1,1) tensors and when (2,0) tensors can't be expressed as outer products

  • Ratzinger
  • · Replies 16 ·
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16

Undergrad Euclidean and Non Euclidean Space?

  • sepulshan
  • · Replies 1 ·
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1

Graduate Worked Problems in Modern Differential Geometry

  • rick1138
  • · Replies 2 ·
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2

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

  • Themetricsystem
  • · Replies 1 ·
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1

Undergrad Equation of a Line in three space question

  • thomasrules
  • · Replies 9 ·
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9

Graduate Definition of a smooth manifold.

  • vanesch
  • · Replies 27 ·
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27

Graduate Connection between physics tensors and algebraic tensoring

  • homology
  • · Replies 7 ·
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7

Graduate Relation between vector field and (n-1)-form for current density

  • mma
  • · Replies 6 ·
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6

Graduate Unifying Curvatures with Riemann Tensor

  • bchui
  • · Replies 2 ·
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2

Graduate Hypersurface equation from parametric form in VN

  • Ed Quanta
  • · Replies 1 ·
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1

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

  • Ogai
  • · Replies 8 ·
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8

Graduate The Geometric Heat Equation-WTF?

  • the.bone
  • · Replies 3 ·
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3

Graduate Geometry - Stereographic projection

  • Pearce_09
  • · Replies 2 ·
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2

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

  • rick1138
  • · Replies 2 ·
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2

Graduate How is topology applied in physics research?

  • rushil
  • · Replies 4 ·
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4

Undergrad Tensor Basics: Understand Tensor or Learn from Websites

  • pastadude
  • · Replies 3 ·
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3

Graduate What Sets Homeomorphic and Isotopic Knots Apart?

  • ComputerGeek
  • · Replies 4 ·
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4

Graduate Explaining the Poincare conjecture in simple terms

  • Ryan Lucas
  • · Replies 3 ·
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3

Graduate Alexander-Briggs notation for knot tables

  • ComputerGeek
  • · Replies 1 ·
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1

Graduate Projective plane as quotient space of a sphere

  • StatusX
  • · Replies 8 ·
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8

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

  • Werg22
  • · Replies 5 ·
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5

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

  • Diophantus
  • · Replies 5 ·
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5

Graduate An extension of the concept of a tensor field

  • Ruslan_Sharipov
  • · Replies 2 ·
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2

Graduate Orthogonal matrices as a manifold with tangent space

  • 'AQF
  • · Replies 3 ·
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3

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

  • 'AQF
  • · Replies 3 ·
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3

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

  • StatusX
  • · Replies 1 ·
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1

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

  • Diophantus
  • · Replies 2 ·
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2

Undergrad Resources for self-studying tensors and topology

  • Limited
  • · Replies 2 ·
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2

Graduate Exterior differential of r³(cos(4θ)dr - r sin(4θ)dθ)

  • Zurtex
  • · Replies 4 ·
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4

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

  • htaati
  • · Replies 4 ·
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4

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

  • htaati
  • · Replies 3 ·
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3

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

  • homology
  • · Replies 21 ·
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21

Undergrad What r the prerequisites for studying diff geo?

  • pavanakumar
  • · Replies 2 ·
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2

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

  • Edwin
  • · Replies 1 ·
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1

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

  • Tzar
  • · Replies 4 ·
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4

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

  • Rousha
  • · Replies 5 ·
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5

Graduate Atlas of Manifold: Is it Countable?

  • Pietjuh
  • · Replies 2 ·
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2

Graduate How to show something is a tensor.

  • Tzar
  • · Replies 2 ·
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2

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

  • Dale12
  • · Replies 4 ·
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4

Graduate How Does Tensor Algebra Apply in Quantum Field Theory?

  • Spinny
  • · Replies 4 ·
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4

Graduate What does A_{[α}B_{β]} mean and how do you write TeX on the forum?

  • bigplanet401
  • · Replies 7 ·
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7

Graduate Is Projective Geometry the Ultimate Form of Kleinian Geometry?

  • Symbreak
  • · Replies 1 ·
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1

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

  • Ed
  • · Replies 2 ·
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2

Graduate Parametrization of a Moebius Strip

  • amcavoy
  • · Replies 10 ·
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10

Undergrad Good Texts for Independent Study

  • TimNguyen
  • · Replies 8 ·
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8

Graduate Radius of curvature formula derivation

  • chandran
  • · Replies 2 ·
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2

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

  • bomba923
  • · Replies 3 ·
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3

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

  • Giuseppe
  • · Replies 1 ·
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1

Graduate Classical proof of Riemann-Roch theorem via period matrices

  • mathwonk
  • · Replies 14 ·
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14

Graduate Surface Area of an N-Dimensional Sphere

  • fizixx
  • · Replies 9 ·
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9

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

  • Ratzinger
  • · Replies 11 ·
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11

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

  • waht
  • · Replies 6 ·
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6

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

  • relinquished™
  • · Replies 2 ·
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2

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

  • HungryChemist
  • · Replies 2 ·
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2

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

  • pimanian
  • · Replies 1 ·
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1

Graduate Find A, B, C for ellipse tangent to x-axis at origin and through P(-1,2)

  • kidia
  • · Replies 5 ·
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5

Undergrad Tensor analysis in curvilinear coordinates

  • hbar314
  • · Replies 2 ·
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2

Graduate Deriving the Implicit Equation of a Rotated Spheroid

  • InfernoSun
  • · Replies 4 ·
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4

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

  • laminatedevildoll
  • · Replies 2 ·
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2

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

  • yourdadonapogostick
  • · Replies 10 ·
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10

Undergrad What is the difference between matrices and tensors?

  • wintercarver
  • · Replies 10 ·
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10

Graduate Finding the projection outline of a rotated spheroid on the xy-plane

  • InfernoSun
  • · Replies 11 ·
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11

Graduate Orientable Manifold with Boundary

  • kakarukeys
  • · Replies 27 ·
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27

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

  • yourdadonapogostick
  • · Replies 1 ·
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1

Graduate Solving Linear Interpolation for 3-D Triangle Edges

  • laminatedevildoll
  • · Replies 1 ·
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1

Graduate If a homeomorphism maps an open subspace of R^n to another, is the image open?

  • kakarukeys
  • · Replies 23 ·
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23

Graduate Implementing a 3-Sphere Model for Molecular Dynamics Simulations

  • quetzalcoatl9
  • · Replies 2 ·
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2

Graduate Funny definition of dimension of a topological space

  • Don Aman
  • · Replies 11 ·
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11

Graduate Does the tensor product of inner product spaces have a natural inner product?

  • Palindrom
  • · Replies 10 ·
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10

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

  • laminatedevildoll
  • · Replies 3 ·
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3

Graduate Flat torus embedding in euclidean space?

  • Highwind
  • · Replies 13 ·
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13

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

  • kleinwolf
  • · Replies 27 ·
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27

Graduate Does E_{ij,k} transform as a tensor when E_{ij} is antisymmetric?

  • learningphysics
  • · Replies 5 ·
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5

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

  • wac03
  • · Replies 5 ·
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5

Graduate Vector parallel to our instantaneous direction of travel

  • touqra
  • · Replies 6 ·
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6

Graduate Question regarding tensors derive acceleration in polar form

  • learningphysics
  • · Replies 2 ·
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2

Undergrad Largest circle inscribed in f(x)=x^2 and f(x)=x^4 with bottom at origin

  • Saint Medici
  • · Replies 5 ·
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5

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

  • isabella
  • · Replies 1 ·
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1

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

  • isabella
  • · Replies 1 ·
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1

Graduate Got the theorem, having trouble with the proof

  • sambo
  • · Replies 5 ·
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5

Undergrad How to satisfy Laplace's equation ?

  • hotel
  • · Replies 6 ·
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6

Graduate Gradient in cylindrical coordinates

  • sid_galt
  • · Replies 1 ·
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1

Graduate Transitioning from aerospace engineering to physics graduate study

  • sniffer
  • · Replies 2 ·
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2

Graduate Is the determinant function an open mapping from R^(n²) to R?

  • kakarukeys
  • · Replies 52 ·
2
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52

Graduate Formula for non-linear differential forms

  • kleinwolf
  • · Replies 14 ·
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14

Graduate Can a smooth transformation relate two surfaces with different metrics?

  • Neitrino
  • · Replies 3 ·
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3

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

  • vic
  • · Replies 4 ·
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4

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

  • quasar987
  • · Replies 8 ·
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8

Graduate Good textbooks on Lie groups and manifolds with worked examples

  • starfield
  • · Replies 14 ·
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14

Graduate Is the Given 4D Manifold Closed?

  • kleinwolf
  • · Replies 17 ·
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17

Undergrad Minimum distance from point to line in 3D space

  • .....
  • · Replies 5 ·
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5

Undergrad What is a tensor and why is it useful?

  • relativitydude
  • · Replies 3 ·
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3

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

  • Sabine
  • · Replies 2 ·
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2

High School The curmufrence and the volume of a sphere

  • cubed
  • · Replies 2 ·
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2

Graduate Quick question on Einstein Notation

  • Autodidact
  • · Replies 6 ·
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6

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

  • Beretta
  • · Replies 6 ·
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6

Graduate How Does Latitude Affect the Compass Angle of Sunrise?

  • chroot
  • · Replies 2 ·
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2

Graduate Hodge Duals and the Interior Product

  • Kane O'Donnell
  • · Replies 20 ·
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20

Graduate Is a homomorphism sending an element

  • Lonewolf
  • · Replies 5 ·
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5