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 Transformation behavior of the gradient

  • joda80
  • · Replies 2 ·
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2

Graduate Is Mean Curvature Invariant Under Coordinate Changes?

  • WWGD
  • · Replies 0 ·
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0

Graduate Is every smooth simple closed curve a smooth embedding of the circle?

  • Only a Mirage
  • · Replies 8 ·
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8

Undergrad Find the point on a line that is X distance away from a plane

  • caibbor
  • · Replies 6 ·
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6

Undergrad Simple curve - not so simple function?

  • Miffymycat
  • · Replies 12 ·
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12

Graduate Ricci curvature of warped AdS spacetime metric

  • darida
  • · Replies 3 ·
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3

Graduate Geometrical interpretation of this coordinate transformation

  • jam_27
  • · Replies 6 ·
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6

Graduate Christoffel Symbol Ansatz for 4D Spacetime

  • darida
  • · Replies 8 ·
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8

High School Is There an Equation for a Rectangular Prism in Cartesian Coordinates?

  • michael pranit
  • · Replies 2 ·
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2

Graduate Integrable vs. Completely Integrable Distributions

  • center o bass
  • · Replies 5 ·
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5

Graduate Find the point on a cone that is farthest in a given direction

  • caibbor
  • · Replies 4 ·
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4

Graduate Constructing a chart with coord. basis equal to given basis at one pt.

  • center o bass
  • · Replies 2 ·
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2

Graduate Why Are Homology Groups Not MUCH Larger?

  • Mandelbroth
  • · Replies 3 ·
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3

Graduate Are left-invariant fields mapped onto the manifold Killing vectors?

  • center o bass
  • · Replies 7 ·
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7

Graduate Condition for a vector field be non-linear

  • Jhenrique
  • · Replies 3 ·
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3

Graduate Solving Two Parabola Problems: Proving & Finding Values

  • varunKanpur
  • · Replies 3 ·
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3

Graduate Vector fields, flows and tensor fields

  • TrickyDicky
  • · Replies 33 ·
2
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33

Graduate Geodesic equations and Christoffel symbols

  • Demon117
  • · Replies 5 ·
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5

Graduate What are independent terms in Magnetic Tensor

  • welshrich
  • · Replies 3 ·
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3

Graduate Tangent vector to curve - notational confusion.

  • center o bass
  • · Replies 1 ·
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1

Graduate Killing vector field => global isomorphisms?

  • center o bass
  • · Replies 8 ·
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8

Graduate Bounding General Shapes with Polygons, Especially Concave

  • downplay
  • · Replies 1 ·
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1

Graduate Questions on Orbifolds S^1/Z_2 and T^2/Z_2

  • "pi"mp
  • · Replies 1 ·
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1

Graduate Recovering a frame field from its connection forms

  • underflow
  • · Replies 1 ·
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1

Graduate How Does the Restricted Three Body Problem Define Motion Manifolds?

  • baxter
  • · Replies 1 ·
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1

Graduate Connecting Lagrangian Density with Field Theory

  • Geometry_dude
  • · Replies 7 ·
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7

Graduate Is the Gradient of a Contravariant Vector a Covariant Vector?

  • nigelscott
  • · Replies 2 ·
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2

Graduate Problem about taking measurements in flat metric spaces

  • haruna
  • · Replies 2 ·
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2

Graduate Virtues of principal/associated bundle formulation of covariant deriv.

  • center o bass
  • · Replies 1 ·
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1

Graduate Why are Invariants so special?

  • NoodleDurh
  • · Replies 1 ·
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1

Graduate Symmetrization of a tensor in spherical coordinate

  • oliveriandrea
  • · Replies 1 ·
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1

Undergrad Curvature of a circle approaches zero as radius goes to infinity

  • BOAS
  • · Replies 5 ·
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5

Graduate How to prove a vector bundle is non-trivial using transition functions

  • nonequilibrium
  • · Replies 2 ·
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2

Undergrad What does it mean to differentiate a coordinate with respect to another coordinate?

  • Jhenrique
  • · Replies 5 ·
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5

Graduate Can Scalar Fields Be Decomposed into Symmetric and Antisymmetric Parts?

  • Jhenrique
  • · Replies 2 ·
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2

Graduate What does the directional derivative operator mean?

  • Jhenrique
  • · Replies 11 ·
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11

Graduate Circulation Definition: Understanding Positive, Null, and Negative Circulation

  • Jhenrique
  • · Replies 6 ·
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6

Graduate Differential forms and differential operators

  • Jhenrique
  • · Replies 5 ·
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5

Graduate Why Can Only Directional Derivatives Be Computed for Scalar Fields?

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Understanding Gradient and Curl: Equations and Directions

  • Jhenrique
  • · Replies 1 ·
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1

Undergrad Lagrangian Multipliers to find maximum and minimum values

  • cooev769
  • · Replies 1 ·
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1

Graduate What is the relationship between Lie algebras and Lie groups on a manifold?

  • Matterwave
  • · Replies 7 ·
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7

Graduate Left-invariant vector field of the additive group of real number

  • AlbertEi
  • · Replies 2 ·
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2

Graduate Is GL(n,C) the biggest complex manifold within GL(2n,R)?

  • nonequilibrium
  • · Replies 1 ·
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1

Graduate Diferentiation and differential operators

  • Jhenrique
  • · Replies 7 ·
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7

Graduate Are all closed forms exact? Are all exact forms closed?

  • Jhenrique
  • · Replies 4 ·
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4

Axis Constrained Collision Distance

  • dotails
  • · Replies 1 ·
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1

Graduate Complete vector field X => X defined on the whole manifold?

  • center o bass
  • · Replies 2 ·
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2

Graduate Generalized Helix: What Do You Think?

  • Abel Cavaşi
  • · Replies 5 ·
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5

Undergrad Finding a Function for a Family of Curves

  • orthogonal
  • · Replies 4 ·
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4

Graduate Surface calculation (no integration)

  • Jhenrique
  • · Replies 7 ·
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7

Graduate Is Fibre Bundles Cartan's Generalization of Klein's Erlagen Program?

  • center o bass
  • · Replies 1 ·
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1

Graduate Fundamental theorem of calculus for surface integrals with vector arguments

  • Jhenrique
  • · Replies 3 ·
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3

Graduate Curl in 2D is a vector or a scalar?

  • Jhenrique
  • · Replies 5 ·
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5

Graduate Why are Lie Subgroups Defined as Immersed Submanifolds?

  • center o bass
  • · Replies 3 ·
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3

Graduate How Can You Find the Inverse of the Exterior Derivative?

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Poor Phrasing of a Lie Group Theorem

  • Mandelbroth
  • · Replies 1 ·
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1

Graduate Derivations vs Directional derivatives

  • center o bass
  • · Replies 4 ·
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4

Graduate Closed ball is manifold with boundary

  • kostas230
  • · Replies 2 ·
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2

Graduate What is the mathematical structure of gravitational lensing shear?

  • zephyr5050
  • · Replies 1 ·
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1

Graduate Unit vectors in different coordinates

  • JasonHathaway
  • · Replies 1 ·
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1

Undergrad Finding the radius of a curved surface

  • mickeyc11
  • · Replies 5 ·
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5

Graduate Originary curves and their mathematical and physical properties

  • Abel Cavaşi
  • · Replies 5 ·
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5

Graduate Is the Modulus of a Tensor Calculated Differently Than a Vector?

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Why Does the Constant Rank Theorem Hold True?

  • center o bass
  • · Replies 1 ·
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1

Graduate Why is a Kähler form not always holomorphic?

  • nonequilibrium
  • · Replies 14 ·
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14

Graduate Cauchy Stress Tensor: Equilibrium Equations

  • ARTjoMS
  • · Replies 1 ·
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1

Graduate Metric and existence of parallel lines

  • ShayanJ
  • · Replies 3 ·
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3

Graduate Geodesic curvature, normal curvature, and geodesic torsion

  • Demon117
  • · Replies 6 ·
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6

Graduate Why Can't Polar Basis Vectors Be Defined as Unit Vectors?

  • epovo
  • · Replies 1 ·
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1

Undergrad Solving Circle Equation with 2 Intersecting Vectors

  • pbayer123
  • · Replies 1 ·
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1

Undergrad Cross products for unit vectors in other coordinate systems

  • AdkinsJr
  • · Replies 4 ·
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4

Graduate Cesàro equation derivatives in polar coordinates

  • Jhenrique
  • · Replies 3 ·
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3

Graduate 2nd tangential angle and torsion

  • Jhenrique
  • · Replies 3 ·
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3

Undergrad Which is orientation of tangential angle in polar coordinates?

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Curvatures at Surface point for non-normal planes

  • Soulagenda
  • · Replies 15 ·
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15

Graduate Operations on circular helices using complex torsion

  • Abel Cavaşi
  • · Replies 2 ·
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2

Graduate R, dr and d²r and curvilinear coordinates

  • Jhenrique
  • · Replies 5 ·
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5

Graduate What is the role of theta in representing polar vectors?

  • Gzyousikai
  • · Replies 3 ·
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3

Undergrad How do you prove Stokes' Theorem?

  • Amsingh123
  • · Replies 5 ·
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5

Graduate Why is Borel's formula true for finite and Lie groups?

  • electroweak
  • · Replies 2 ·
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2

Graduate Existence of Hodge Dual: obvious or non-trivial?

  • nonequilibrium
  • · Replies 1 ·
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1

Graduate Is there a theorem for the Laplacian like for gradient, curl, and divergence?

  • Jhenrique
  • · Replies 5 ·
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5

Graduate Parallel transport around a loop

  • dEdt
  • · Replies 2 ·
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2

Graduate What does it mean for a manifold to admit a metric?

  • center o bass
  • · Replies 3 ·
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3

Graduate Charts on submersions (manifolds).

  • center o bass
  • · Replies 9 ·
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9

Ernesto's question at Yahoo Answers regarding finding a locus of points

  • MarkFL
  • · Replies 1 ·
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1

Graduate Understanding Triply Periodic Surfaces: Translations and Invariance?

  • Demon117
  • · Replies 1 ·
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1

Graduate What are the components of the vector d²r in relation to dr?

  • Jhenrique
  • · Replies 8 ·
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8

Graduate Symmetry (killing vector) preserving diffeomorphisms

  • center o bass
  • · Replies 1 ·
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1

Undergrad Fundamental theorem of calculus for surface integrals?

  • Jhenrique
  • · Replies 9 ·
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9

Graduate Yet more elementary questions about the tangent space

  • orion
  • · Replies 25 ·
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25

Graduate Derivative of Unit Vector in a Rotating Frame

  • Jhenrique
  • · Replies 12 ·
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12

Undergrad Is it true that ##t=n\times b##?

  • DeadOriginal
  • · Replies 1 ·
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1

Graduate Formulating a Method of Steepest Ascent on Lie Groups

  • Mandelbroth
  • · Replies 3 ·
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3

Graduate Conditions for Solution to Pullback Equation on Forms?

  • WWGD
  • · Replies 1 ·
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1

Group velocity of extraordinary waves in uniaxial crystals

  • Joystar77
  • · Replies 1 ·
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1

Graduate Example of a topological manifold without smooth transition functions.

  • center o bass
  • · Replies 15 ·
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15

Graduate Program Computing Wedge of Differential Forms?

  • WWGD
  • · Replies 2 ·
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2

Graduate Why Is My Covariant Derivative Result Incorrect?

  • Jhenrique
  • · Replies 1 ·
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1