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 Solving a 'skew' quadrilateral for vertex position.

  • athuss
  • · Replies 3 ·
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3

Graduate Why is the gradient of a function considered a one form in Schutz's book on GR?

  • GarageDweller
  • · Replies 15 ·
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15

Undergrad Calculate Position - Angle Difference of Arrival

  • murrdpirate0
  • · Replies 4 ·
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4

Graduate Evenly spaced points in oddly shaped volume?

  • blrnd
  • · Replies 4 ·
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4

Graduate Understanding Minimal Surfaces: QFT Math Prerequisites

  • JPBenowitz
  • · Replies 5 ·
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5

Graduate Integer Cohomology of Real Infinite-Dimensional Grassmann Manifold

  • lavinia
  • · Replies 4 ·
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4

Graduate Cat vs Mouse (bipartite graphs) - can mouse evade capture?

  • KOSS
  • · Replies 2 ·
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2

How to Solve Vector Equations and Find Distances in Analytic Geometry?

  • Fantini
  • · Replies 1 ·
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1

Graduate Algebraic Topology - Retractions and Homomorpisms Induced by Inclusions

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Killing vectors for a given Kahler potential

  • L0r3n20
  • · Replies 3 ·
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3

Graduate Algebraic Topology - Fundamental Group and the Homomorphism induced by h

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Calculating the Z2 cohomology of the Klein Bottle using intersections

  • lavinia
  • · Replies 3 ·
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3

Graduate Is the Ratio of Circumference to Diameter Always Pi in Non-Euclidean Space?

  • Allojubrious
  • · Replies 11 ·
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11

Graduate How does the proof of Sard's theorem utilize vector spaces and planes?

  • brydustin
  • · Replies 1 ·
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1

Graduate Computing arc length in Poincare disk model of hyperbolic space

  • owlpride
  • · Replies 4 ·
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4

Graduate Exterior algebra and n-dimensional volumes

  • coquelicot
  • · Replies 26 ·
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26

Graduate Is Every Element of n-Torus DeRham Cohomology Independent?

  • Sina
  • · Replies 3 ·
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3

Graduate What is the Klein Four-Group Geometry and Its Applications?

  • JeremyEbert
  • · Replies 57 ·
2
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57

Graduate Orthogonal Lines and their line element

  • Vorde
  • · Replies 2 ·
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2

Undergrad How Can You Calculate the Center of Rotation in 3D Space?

  • yasith
  • · Replies 1 ·
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1

Graduate How Does a Vector Transform Across Different Charts on a Manifold?

  • sadegh4137
  • · Replies 1 ·
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1

Graduate Euler Angles - Why Post Multiplication

  • phiby
  • · Replies 4 ·
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4

Graduate Why Does the Second Equality Hold in Multi-Linear Algebra?

  • brydustin
  • · Replies 1 ·
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1

Graduate Is There Such a Thing as DeRham Homology?

  • WWGD
  • · Replies 10 ·
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10

Graduate How Can I Understand the Geometrical Construction of Klein's Quartic?

  • mery2
  • · Replies 1 ·
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1

Undergrad How Do You Define an Axis with Three Unit Vectors?

  • mattsap
  • · Replies 3 ·
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3

Graduate Simplify Condition for Chord Length Equals Angle?

  • DuncanM
  • · Replies 1 ·
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1

Graduate Poincaré disk: metric and isometric action

  • Sajet
  • · Replies 6 ·
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6

Graduate Second fundamental form of surface with diagonal metric

  • Sina
  • · Replies 8 ·
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8

Graduate Understanding Monodromy Map of a Covering Space: Can Anyone Help?

  • angy
  • · Replies 3 ·
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3

Graduate Rao: Proposition 1.2.4. Superfluous section of proof?

  • Rasalhague
  • · Replies 1 ·
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1

Graduate The singular points on f = x^2 y - x y on a plane

  • naturemath
  • · Replies 5 ·
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5

Undergrad Distance of a point to an Ellipsoid

  • jaykavathe
  • · Replies 1 ·
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1

Graduate Understanding the Lie Derivative of Tensors: A Step-by-Step Approach

  • sadegh4137
  • · Replies 1 ·
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1

Graduate Deformation retraction of plane RP2

  • semigroups
  • · Replies 23 ·
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23

Graduate What is the Definition of C1-Close Curve in Whitney Topology?

  • Ad123q
  • · Replies 1 ·
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1

Graduate Orthogonality of Absolute Derivative

  • rbwang1225
  • · Replies 1 ·
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1

Graduate What's relation between factorial and tensor components.?

  • aditya23456
  • · Replies 4 ·
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4

Undergrad Triangle Inequalities Relationship

  • ait.abd
  • · Replies 5 ·
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5

Graduate Are Homotopic Maps of the n-Sphere Antipodal?

  • alexfloo
  • · Replies 8 ·
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8

Graduate Tensor fields and multiplication

  • Kontilera
  • · Replies 4 ·
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4

Graduate What are the properties of orbifolds and how do they differ from manifolds?

  • scottbekerham
  • · Replies 10 ·
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10

Graduate How to verify if a mapping is quotient.

  • SVD
  • · Replies 3 ·
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3

Graduate Inversion w.r.t. a sphere: Operator

  • neelakash
  • · Replies 18 ·
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18

Graduate Stoke's theorem and normal vectors

  • BrianC12
  • · Replies 12 ·
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12

Graduate Cohomology with coefficients in a sheaf

  • feuxfollets
  • · Replies 3 ·
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3

Graduate Can you explain dual tensors and tensor densities with a simple example?

  • aditya23456
  • · Replies 4 ·
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4

Graduate Varying Energy in a Schwartzschild Metric

  • Meselwulf
  • · Replies 2 ·
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2

Graduate Quickly: Multlinearity of exterior derivative, and proof of invariant formula

  • ianhoolihan
  • · Replies 3 ·
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3

Undergrad Help with a Geometry Problem - Calculating The Radius of a Curve

  • tomtomtom1
  • · Replies 1 ·
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1

Undergrad What is the shape of the surface defined by a(x²+y²)+bz²=c?

  • pcm
  • · Replies 4 ·
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4

Graduate How can I construct a Riemann surface from branch data?

  • angy
  • · Replies 3 ·
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3

Graduate What is the significance of the modulus of a Riemann surface?

  • theorem4.5.9
  • · Replies 9 ·
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9

Undergrad 1-point perspective Room with 2- and 3-point Objects possible?

  • Robert_N
  • · Replies 11 ·
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11

Undergrad Poincare Conjecture: Explaining Lower Dimension Equivalent

  • Phyzwizz
  • · Replies 2 ·
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2

Graduate Morse homology of a tilted torus.

  • MathematicalPhysicist
  • · Replies 3 ·
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3

Graduate Visualising singular cohomology using cap product.

  • Jamma
  • · Replies 1 ·
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1

Graduate How to Calculate the Axis of Rotation in 3D Space?

  • yasith
  • · Replies 16 ·
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16

Graduate Deriving Elastica Equation: Bernoulli/Newton

  • hushish
  • · Replies 6 ·
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6

Undergrad Checking if a point is on an arc, defined by two vectors

  • deluksic
  • · Replies 14 ·
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14

Graduate Does the metric tensor only depend on the coordinate system used?

  • HilbertSpace
  • · Replies 17 ·
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17

Graduate Calculating Riemann Curvature Tensor: Faster Methods?

  • HilbertSpace
  • · Replies 1 ·
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1

Graduate How Do Velocity and Displacement Vectors Transform in Plane Polar Coordinates?

  • ShayanJ
  • · Replies 7 ·
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7

Graduate What are the best resources for beginners to learn about Holonomy Groups?

  • LightKage
  • · Replies 2 ·
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2

Graduate How Do Indices Function in Tensor Notation?

  • Miloslav
  • · Replies 3 ·
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3

Undergrad FInd the Vector passing thru a point and parallel to two points in a plane

  • kailsen
  • · Replies 2 ·
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2

Graduate Topologising RP2 using open sets in R3

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad How to make the total length of a trail as short as possible?

  • moonman239
  • · Replies 9 ·
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9

High School How to draw a logarithmic spiral

  • TalonD
  • · Replies 2 ·
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2

Graduate Levi-cevita parallel propagation on a sphere

  • ianhoolihan
  • · Replies 13 ·
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13

Graduate Euler characteristic of complex projective plane

  • jgens
  • · Replies 7 ·
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7

Graduate Limiting the placement of covering rectangle with smaller rectangles algorithm?

  • the_anomaly
  • · Replies 2 ·
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2

Graduate Developing a General Formula for a family of Curve Shapes

  • jmosk
  • · Replies 4 ·
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4

Graduate Vectors, Covectors & Tangentvector in Manifolds without Metric

  • Kontilera
  • · Replies 2 ·
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2

Graduate Understanding Minimal Surfaces: Laplace Pressure of a Capillary Bridge

  • lionelwang
  • · Replies 6 ·
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6

Graduate What are projective transformations?

  • A_B
  • · Replies 5 ·
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5

Graduate Can 5th order equations be solved by means other than radicals?

  • meldraft
  • · Replies 1 ·
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1

Undergrad What is the solution to Dido's problem?

  • pilpel
  • · Replies 1 ·
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1

Undergrad What is the purpose of the normal equation of the plane?

  • Alshia
  • · Replies 8 ·
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8

Graduate Question on energy displacement.

  • MathematicalPhysicist
  • · Replies 1 ·
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1

Graduate How to create normal Riemann surface for cubic?

  • jackmell
  • · Replies 8 ·
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8

Graduate Reference for simplicial homology and cohomology

  • lavinia
  • · Replies 23 ·
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23

Graduate Is Horn-torus a valid genus-1 Riemann Surface?

  • jackmell
  • · Replies 2 ·
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2

Graduate Question on tensor notation in group theory

  • BWV
  • · Replies 1 ·
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1

Graduate Interpretation of torsion vs riemann tensor

  • ianhoolihan
  • · Replies 24 ·
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24

Undergrad Stuck on a 3D coordinate geometry problem

  • yasith
  • · Replies 11 ·
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11

High School Why Do 3D Coordinates Include Four Parameters?

  • marensi
  • · Replies 2 ·
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2

Undergrad What are some solved exercises on graph connectedness in graph theory?

  • Deimantas
  • · Replies 1 ·
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1

Graduate Index Notation: ∂_i 1/r = -x_i/r^3?

  • ellocomateo
  • · Replies 2 ·
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2

Graduate Smooth Homotopy, Regular Values (Milnor)

  • Sina
  • · Replies 4 ·
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4

Graduate Is e an Accumulation Point in This Topology?

  • Arian.D
  • · Replies 3 ·
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3

Graduate Path ordered integral over simplices?

  • ianhoolihan
  • · Replies 3 ·
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3

Graduate Help finishing connectedness proof.

  • Mister Eric
  • · Replies 1 ·
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1

Graduate 4 component spinor isomorphic to S^7?

  • Spinnor
  • · Replies 3 ·
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3

Graduate Parallel propagator and covariant derivative of vector

  • ianhoolihan
  • · Replies 5 ·
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5

Graduate Rigged Hilbert Space: Algebraic v.s. Continuous Dual Space

  • Rasalhague
  • · Replies 5 ·
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5

Graduate Mapping contours over normal Riemann surfaces

  • jackmell
  • · Replies 5 ·
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5

Graduate Xyx^-1y^-1 a Lie group homomorphism?

  • Sajet
  • · Replies 2 ·
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2

Graduate Linear change of coordinates preserving a certain property

  • naturemath
  • · Replies 1 ·
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1

Undergrad Is a Helix One-Dimensional?

  • phinds
  • · Replies 18 ·
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18