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 Cross between helicoid, complex plane wave

  • Spinnor
  • · Replies 5 ·
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5

Undergrad Where to Learn Involute Curve?

  • askor
  • · Replies 4 ·
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4

Graduate Trouble understanding ##g^{jk}\Gamma^{i}{}_{jk}##

  • shooride
  • · Replies 4 ·
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4

Graduate A general 2-form - Colley Chapter 8, Section 8.1

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Physical motivation for integrals over scalar field?

  • Feynman's fan
  • · Replies 2 ·
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2

Graduate Simple/Basic Example on Wedge Products

  • Math Amateur
  • · Replies 5 ·
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5

Graduate What is the mapping between the hyperriemann sphere and the complex plane?

  • EinsteinKreuz
  • · Replies 4 ·
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4

Undergrad What is the smoothness condition in vector calculus derivatives?

  • Hornbein
  • · Replies 15 ·
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15

Graduate More (VERY BASIC) Questions on Example on Wedge Products

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Covariant and contravariant basis vectors /Euclidean space

  • meteo student
  • · Replies 11 ·
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11

Graduate Non-Euclidean geometry and the equivalence principle

  • "Don't panic!"
  • · Replies 11 ·
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11

Graduate Notation in Ch. 10 of Nakahara

  • Bballer152
  • · Replies 9 ·
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9

Graduate Is my understanding of the second-rank four-tensor correct?

  • jack476
  • · Replies 2 ·
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2

Graduate Rotations in differential geometry

  • meteo student
  • · Replies 30 ·
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Graduate Compute Translation, Rotation in SE(3) with Chasles Theorem

  • hunt_mat
  • · Replies 3 ·
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3

Graduate Walk a 3-sphere w/Hopf Fibration: Parameterization

  • Hornbein
  • · Replies 2 ·
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2

Graduate Curl of tensor * non-constant vector

  • refind
  • · Replies 1 ·
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1

Graduate N-sphere as manifold without embedding

  • JonnyG
  • · Replies 26 ·
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26

Graduate Unique smooth structure on Euclidean space

  • JonnyG
  • · Replies 13 ·
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13

Graduate Envelope of a parametric family of functions

  • Icaro Lorran
  • · Replies 1 ·
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1

Graduate Euler angles in latitude longitude space

  • meteo student
  • · Replies 1 ·
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1

Undergrad Coordinate transformation from spherical to rectangular

  • TheArun
  • · Replies 14 ·
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14

Graduate Troubleshooting N-Spherical Cap Area Formula

  • olgerm
  • · Replies 3 ·
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3

Graduate Intersection of general plane with quadric surface

  • swampwiz
  • · Replies 1 ·
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1

What are the practical applications of differential geometry?

  • mathmari
  • · Replies 3 ·
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3

Graduate Non-Euclidean area defined by three points on a sphere

  • 24forChromium
  • · Replies 10 ·
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10

Graduate Jet Prolongation Formulas for Lie Group Symmetries

  • Twigg
  • · Replies 7 ·
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7

Graduate Spherical vectors and rotation of axes

  • meteo student
  • · Replies 2 ·
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2

Graduate Quadratic Conformal Mapping with Parameters | QP

  • benpaulthurston
  • · Replies 4 ·
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4

Graduate How do I use the geodesic equation for locations on earth

  • NihalRi
  • · Replies 14 ·
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14

Graduate Followup: pi on curved surfaces

  • DaveC426913
  • · Replies 23 ·
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23

Graduate Opposite "sides" of a surface - Differential Geometry.

  • thehangedman
  • · Replies 5 ·
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5

Graduate Velocity in spherical polar coordinates

  • meteo student
  • · Replies 2 ·
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2

Graduate Contravariant and covariant vectors

  • Sonia AS
  • · Replies 7 ·
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7

Graduate A question about differential form

  • 1591238460
  • · Replies 8 ·
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8

Graduate Two questions for vector bundles

  • 1591238460
  • · Replies 18 ·
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18

Graduate Vector Rotation About Arbitrary Axis

  • MD Aminuzzaman
  • · Replies 8 ·
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8

Graduate The restriction of differential form

  • 1591238460
  • · Replies 10 ·
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10

Graduate How to Calculate Gauss Curvature from a Mesh Surface?

  • Omega0
  • · Replies 2 ·
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2

Graduate Why is a conserved vector field a gradient of a certain func

  • Za Kh
  • · Replies 3 ·
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3

Graduate Tangent spaces at different points on a manifold

  • "Don't panic!"
  • · Replies 63 ·
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Graduate How Do Indices Affect Tensor Notation?

  • spaghetti3451
  • · Replies 7 ·
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7

Graduate Calculating Volume of Arbitrary Cross-Section Triangles

  • Cokemaster
  • · Replies 17 ·
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17

Graduate Differential Geometry page 193 Nakahara

  • smallgirl
  • · Replies 17 ·
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17

Graduate Writing a general curve on a manifold given a metric

  • wotanub
  • · Replies 7 ·
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7

Undergrad What is the radius of curvature formula for an ellipse at slope = 1?

  • jjredfish
  • · Replies 29 ·
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29

Graduate Why phi component is not taken into account for vector R ?See attachment.

  • Saurabh Sharma
  • · Replies 2 ·
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2

Graduate Engineering a body with an intrinsic curvature

  • geordief
  • · Replies 16 ·
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16

Graduate Meaning of Curl from stokes' theorem

  • Titan97
  • · Replies 3 ·
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3

Graduate Understanding Index Notation: Simplifying Tensor and Vector Equations

  • nabber
  • · Replies 8 ·
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8

Graduate Transverse Vector: Definition & Meaning

  • Harel
  • · Replies 1 ·
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1

Undergrad Is There a Mistake in the Hyperbolic Paraboloid Curve Demonstration?

  • mohamed el teir
  • · Replies 1 ·
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1

Graduate Are Skew Lines Considered Perpendicular in 3D with Parallel Vectors?

  • mohamed el teir
  • · Replies 6 ·
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6

Graduate Interpreting Curl in Vector Fields: ∇×v

  • Titan97
  • · Replies 1 ·
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1

Graduate Meaning of isomorphism/diffeomorphism ## f: R^n\to M^m##

  • shooride
  • · Replies 36 ·
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36

Graduate Calculating mixed partial derivatives on a 3D mesh

  • KareemErgawy
  • · Replies 6 ·
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6

Graduate Geometrical meaning of Curl(Gradient(T))=0

  • Titan97
  • · Replies 3 ·
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3

Graduate Coordinate transformation - NED and ECEF frames

  • 9988776655
  • · Replies 2 ·
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2

Undergrad Given a vector, how to compute orthogonal plane

  • MF2
  • · Replies 4 ·
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4

Graduate Finding the sine of the angle between 2 rays

  • Matterwave
  • · Replies 16 ·
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16

Graduate Taylor expansion of the square of the distance function

  • shooride
  • · Replies 9 ·
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9

Graduate Is x^2 + y^2 = 4R^2 a Cylinder or a Circle in 3D Space?

  • whatisreality
  • · Replies 8 ·
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8

Graduate Is There a Solution to the Inconvenient Expression for Area and Element of Area?

  • Bruno Tolentino
  • · Replies 1 ·
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1

Graduate ##x+y## on a Riemannian manifold

  • shooride
  • · Replies 22 ·
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22

Graduate Geometry on a Sphere: Euclidean or Something Else?

  • geordief
  • · Replies 12 ·
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12

Graduate Calculate the distance travelled in a moving circumference?

  • pabilbado
  • · Replies 4 ·
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4

Graduate Ricci rotation coefficients and non-coordinate bases

  • "Don't panic!"
  • · Replies 10 ·
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10

Graduate How Can I Simplify an Equation Involving Levi-Civita Tensors and Indices?

  • PhyAmateur
  • · Replies 8 ·
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8

Graduate Manifolds: extrinsic and intrinsic

  • shereen1
  • · Replies 5 ·
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5

Undergrad 3D object represent with primitive shapes

  • shanky
  • · Replies 5 ·
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5

Graduate Riemannian Metric Tensor & Christoffel Symbols: Learn on R2

  • shanky
  • · Replies 7 ·
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7

Graduate Types of Rotations - Hi Everybody, Ask Your Questions Here

  • Adrian555
  • · Replies 5 ·
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5

Graduate Lie derivative of tensor field with respect to Lie bracket

  • "Don't panic!"
  • · Replies 4 ·
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4

Graduate Curved surfaces that do not preserve area

  • diegzumillo
  • · Replies 11 ·
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11

Graduate Angle and trig definitions in curved space

  • newjerseyrunner
  • · Replies 2 ·
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2

Undergrad Help with David Bachman's A Geometric Approach to Differential Forms, 2nd Ed.

  • nearc
  • · Replies 5 ·
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5

Graduate Difference between Manifolds and Non-Euclidean spaces

  • mikeeey
  • · Replies 9 ·
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9

Graduate Vector fields transverse to the boundary of a manifold

  • jford1906
  • · Replies 6 ·
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6

Graduate Proving K+U is constant with tensor notation.

  • davidbenari
  • · Replies 1 ·
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1

Graduate Charting Manifolds: Tips & Techniques

  • mikeeey
  • · Replies 9 ·
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9

Graduate Riemannin generalization of the Taylor expansion

  • shooride
  • · Replies 3 ·
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3

Graduate How to relate the Ehresmann connection to connection 1-form?

  • xXEhresmannXx
  • · Replies 3 ·
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3

Graduate Lie derivative of two left invariant vector fields

  • konik13
  • · Replies 3 ·
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3

Graduate Logic behind definition of Reparametrization

  • Raman Choudhary
  • · Replies 2 ·
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2

Graduate What are the Discret Subgroups of O(1,3)?

  • Andre' Quanta
  • · Replies 3 ·
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3

Graduate Understanding fractional and higher dimensions

  • PcumP_Ravenclaw
  • · Replies 13 ·
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13

Graduate Why is ##x = r \sin{\phi} \cos{\theta}## in spherical coordinates?

  • PFuser1232
  • · Replies 26 ·
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26

Graduate Product of a symmetric and antisymmetric tensor

  • stedwards
  • · Replies 4 ·
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4

Graduate Curvature implying Closedness in N dimensions

  • jfizzix
  • · Replies 4 ·
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4

Graduate Finding Coefficients of Orthogonal Quadric Equations

  • Bruno Tolentino
  • · Replies 6 ·
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6

Undergrad Drawing Curves with Conic Sections

  • Bruno Tolentino
  • · Replies 3 ·
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3

Graduate Calculating the Solid Angle Subtended by a Disc: How to Find ω?

  • brotherbobby
  • · Replies 3 ·
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3

Graduate How Do Tangents Differ Between y²=4ax and x²=4ay?

  • fireflies
  • · Replies 6 ·
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6

Undergrad What type of coordinate system?

  • shanepitts
  • · Replies 1 ·
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1

Graduate Are Global and Local Coordinate Charts Different in Differentiable Manifolds?

  • mikeeey
  • · Replies 16 ·
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16

Graduate Why Does (\partial_{\mu}\phi)^2 Equal (\partial_{\mu}\phi)(\partial^{\mu}\phi)?

  • noahcharris
  • · Replies 3 ·
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3

Undergrad Center of a irregular hexahedra given the vertices

  • pyroknife
  • · Replies 7 ·
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7

Graduate Is This Contraction of a Tensor Allowed?

  • Physicist97
  • · Replies 4 ·
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4

Graduate Can someone verify this definition for Weyl tensor?

  • space-time
  • · Replies 7 ·
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7

Graduate Questions about the differential

  • orion
  • · Replies 32 ·
2
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32