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 Stokes' Theorem and Curvature on a Torus

  • lichen1983312
  • · Replies 7 ·
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7

Undergrad Metric tensor : raising/lowering indices

  • tb87
  • · Replies 2 ·
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2

Undergrad Levi-Civita properties in 4 dimensions

  • Phys pilot
  • · Replies 1 ·
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1

Undergrad Understanding the Derivation of the Metric Tensor

  • kidsasd987
  • · Replies 1 ·
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1

Undergrad Proving Stokes' Theorem: General Cases and the Fundamental Theorem of Calculus

  • davidge
  • · Replies 9 ·
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9

Undergrad Mean and Gaussian curvature for a Gaussian 'hill' seem wrong

  • Zaent
  • · Replies 6 ·
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6

Undergrad Problem when solving example with differential forms

  • davidge
  • · Replies 4 ·
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4

Undergrad Integrals: Why Change from M to $\phi(M)$?

  • davidge
  • · Replies 3 ·
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3

Graduate Extracting Tensor Algebra Term with SU(N) Generators and Numbers

  • spaghetti3451
  • · Replies 1 ·
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1

Graduate Is there a natural paring between homology and cohomology?

  • lichen1983312
  • · Replies 19 ·
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19

Undergrad Is Second rank tensor always tensor product of two vectors?

  • arpon
  • · Replies 2 ·
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2

Graduate Can the Frenet Serret Frame Aid in Arc Length Parameterizations?

  • rabbed
  • · Replies 19 ·
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19

Graduate Is the Gradient a Covector and the Cross Product a Pseudovector?

  • zwierz
  • · Replies 20 ·
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20

The tangent and the normal to the conic

  • debrajr
  • · Replies 1 ·
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1

Find the equation of the conicoid

  • debrajr
  • · Replies 1 ·
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1

Undergrad Worked example on a covariant vector transformation

  • Dyatlov
  • · Replies 4 ·
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4

Undergrad Curvature forms and Riemannian curvatures of connections

  • RockyMarciano
  • · Replies 53 ·
2
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53

Graduate Diffeomorphisms & the Lie derivative

  • Frank Castle
  • · Replies 9 ·
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9

Undergrad Lie groups left invariant vector fields

  • Mikeey aleex
  • · Replies 3 ·
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3

Graduate About the nodal line in defining Euler angles

  • ftft
  • · Replies 3 ·
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3

Graduate Pullback and Pushforward in Manifolds: Why Do We Do It?

  • observer1
  • · Replies 4 ·
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4

Formula for Ellipse 'Change of Distance by Change of Theta'?

  • SquishyWeRRa
  • · Replies 1 ·
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1

Undergrad Chart coordinate maps of topological manifolds

  • Mikeey aleex
  • · Replies 1 ·
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1

Undergrad Term: generalization of parallel curves to 3D

  • nomadreid
  • · Replies 8 ·
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8

Undergrad Norm of Laplacian Let: Formula for | ∇X|² in Coordinates

  • user2010
  • · Replies 2 ·
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2

Graduate Conformal flatness of Riemannian manifolds

  • RockyMarciano
  • · Replies 5 ·
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5

Graduate Tangent Bundle: Why It's Important

  • observer1
  • · Replies 2 ·
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2

High School What would things look like if PI = 3.

  • phillovix
  • · Replies 5 ·
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5

Undergrad Ave length of intersection of all lines through a unit cube

  • bahamagreen
  • · Replies 4 ·
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4

High School About the surface area of a prolate ellipsoid

  • Tahmeed
  • · Replies 3 ·
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3

Graduate Methods to interpolate surfaces from gradient field?

  • grumpymrgruff
  • · Replies 1 ·
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1

Undergrad Winding number for a point that lies over a closed curve

  • pigna
  • · Replies 4 ·
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4

Undergrad Here There be Dragons in Sympletic Geometry

  • jedishrfu
  • · Replies 2 ·
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2

Graduate Principal bundle triviality, groups and connections

  • RockyMarciano
  • · Replies 6 ·
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6

Undergrad Determining Coordinate Transformations for Cloaking Device

  • Lizard
  • · Replies 1 ·
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1

Undergrad Why is the area of a circular cap on a sphere not equal to πr^2?

  • JohnnyGui
  • · Replies 11 ·
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11

Undergrad Ricci curvatures determine Riemann curvatures in 3-dimension

  • tommyxu3
  • · Replies 3 ·
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3

Undergrad Difference between 1-form and gradient

  • meteo student
  • · Replies 14 ·
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14

Undergrad Deriving Frenet-Serret Formulas: Why -τᴿ?

  • Arya Prasetya
  • · Replies 3 ·
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3

Undergrad Is There a Faster Way to Prove Smoothness on Manifolds?

  • JonnyG
  • · Replies 2 ·
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2

Undergrad Conservation of dot product with parallel transport

  • fab13
  • · Replies 9 ·
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9

Graduate Very basic question about cohomology.

  • lichen1983312
  • · Replies 7 ·
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7

Graduate Understanding Exact vs. Closed Forms for Mechanical Engineers

  • observer1
  • · Replies 3 ·
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3

Graduate The meaning of an integral of a one-form

  • observer1
  • · Replies 9 ·
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9

Graduate Period matrix of the Jacobian variety of a curve

  • GogoJS
  • · Replies 2 ·
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2

Graduate A question about split short exact sequence

  • lichen1983312
  • · Replies 21 ·
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21

Graduate What Determines the Degree of the Gauss Map in Differential Geometry?

  • spaghetti3451
  • · Replies 5 ·
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5

Graduate Two cones connected at their vertices do not form a manifold

  • Heisenberg1993
  • · Replies 14 ·
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14

Undergrad Why Are Connection 1 Forms Essential in Principal G-Bundles?

  • hideelo
  • · Replies 3 ·
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3

Undergrad How is a manifold locally Euclidean?

  • FallenApple
  • · Replies 10 ·
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10

Graduate Metric on ℝ^2 Invariant under Matrix Transformations

  • FrederikPhysics
  • · Replies 1 ·
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1

Graduate Oscillating Plane and Z axis - Energy Balance

  • Questionable Thought
  • · Replies 1 ·
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1

Undergrad What does this notation mean? (suffix/prefix on tensors?)

  • sa1988
  • · Replies 2 ·
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2

Graduate Difference between free G-action and effective G-action?

  • pellman
  • · Replies 1 ·
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1

Undergrad Computing the Weingarten Map L by raising an index

  • Leo Mar
  • · Replies 2 ·
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2

Graduate How Does the Volume Form on the Unit Sphere Relate to Its Position Vector?

  • spaghetti3451
  • · Replies 7 ·
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7

High School Calculating a straight line within a sphere

  • DaveC426913
  • · Replies 7 ·
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7

Graduate Why the Chern numbers (integral of Chern class) are integers?

  • lichen1983312
  • · Replies 12 ·
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12

High School Curve where both x and y approach infinity

  • Pjpic
  • · Replies 6 ·
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6

Undergrad Commutator of covariant derivatives

  • naima
  • · Replies 5 ·
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5

Undergrad Question About Curvilinear Cooridnates

  • TonyEsposito
  • · Replies 2 ·
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2

Graduate Theory of Surfaces and Theory of Curves Relationship

  • ltkach2015
  • · Replies 5 ·
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5

Undergrad How do I calculate the surface area of a rotated curve?

  • ddddd28
  • · Replies 2 ·
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2

Graduate Differential forms and vector calculus

  • spaghetti3451
  • · Replies 10 ·
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10

Undergrad Meaning of the sign of the geodesic curvature

  • Leo Mar
  • · Replies 3 ·
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3

Graduate Interior products, exterior derivatives and one forms

  • spaghetti3451
  • · Replies 3 ·
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3

Undergrad Torsion on cylinder described differentially

  • MicroCosmos
  • · Replies 2 ·
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2

Undergrad How to write a Vector Field in Cylindrical Co-ordinates?

  • greswd
  • · Replies 4 ·
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4

Graduate Torsion forms and particle physics

  • itssilva
  • · Replies 5 ·
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5

Graduate Line integrals of differential forms

  • spaghetti3451
  • · Replies 1 ·
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1

Graduate Definition of the Lie derivative

  • spaghetti3451
  • · Replies 2 ·
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2

Undergrad How are Vectors described in Bispherical Coordinates?

  • tade
  • · Replies 10 ·
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10

Graduate Square of the exterior derivative

  • spaghetti3451
  • · Replies 10 ·
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10

Undergrad Prove ∇(A x B) = (∇ x A)⋅B - (∇ x B)⋅A where A,B are vectors

  • goggles31
  • · Replies 5 ·
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5

Graduate Ricci Form Notation: Need Help Understanding

  • lichen1983312
  • · Replies 3 ·
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3

Graduate Action of a vector on the pull-back of a function

  • spaghetti3451
  • · Replies 1 ·
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1

Undergrad Make a Pseudo-Riemannian Metric Conformal

  • tommyxu3
  • · Replies 3 ·
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3

Undergrad What shape is the ecliptic as seen from Earth?

  • Pjpic
  • · Replies 1 ·
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1

Graduate Unique separation of the vertical and horizontal spaces?

  • lichen1983312
  • · Replies 2 ·
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2

Undergrad (Index Notation) Summing a product of 3 numbers

  • throneoo
  • · Replies 4 ·
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4

High School Trying to represent a written geometrical description

  • CollinsArg
  • · Replies 1 ·
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1

High School Deriving the Polar of a Point on a Conic

  • Appleton
  • · Replies 4 ·
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4

Undergrad Levi-Civita: very small problem, need two steps explained

  • Waxterzz
  • · Replies 3 ·
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3

Undergrad Confusion on Bianchi Identity proof

  • Dazed&Confused
  • · Replies 2 ·
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2

Undergrad Lie derivative of a differential form

  • daxowax
  • · Replies 2 ·
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2

Graduate Existence of Complex Structures and Characteristic Classes

  • WWGD
  • · Replies 4 ·
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4

Graduate Maurer–Cartan forms for a matrix group?

  • lichen1983312
  • · Replies 2 ·
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2

Undergrad Describing position on an ellipse as a function of angle

  • tomwilliam2
  • · Replies 2 ·
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2

Graduate Tangent Bundle questions about commutative diagram

  • orion
  • · Replies 20 ·
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20

Undergrad Notation in Spivak's Calculus on Manifolds

  • Z90E532
  • · Replies 1 ·
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1

Undergrad Conformal geometry vs. projective geometry

  • Lapidus
  • · Replies 1 ·
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1

Finding Distinct and Singular Normals for a Parabola

  • Theia
  • · Replies 2 ·
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2

Undergrad How directrix for other than parabola?

  • symbolipoint
  • · Replies 1 ·
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1

First Approach to Differential Forms

  • Math Amateur
  • · Replies 10 ·
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10

Undergrad Intuition on divergence and curl

  • cgiustini
  • · Replies 3 ·
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3

Undergrad Questions about gradient and scalar product

  • space-time
  • · Replies 1 ·
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1

High School Base space Minkowski, fiber is S^1, total spaces?

  • Spinnor
  • · Replies 10 ·
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10

Undergrad Rotation and Translation coordinates

  • FrederikPhysics
  • · Replies 5 ·
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5

Undergrad Example of computing geodesics with 2D polar coordinates

  • fab13
  • · Replies 1 ·
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1

Undergrad Finding shortest distance between skew lines, checking work.

  • RoboNerd
  • · Replies 15 ·
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15