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

What Is the Optimal Geometry for a Concrete Column Supporting 1250 Tonnes?

  • Dethrone
  • · Replies 1 ·
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Graduate Why is there maximally 1/2 n(n+1) killing vectors?

  • center o bass
  • · Replies 1 ·
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Graduate Riemannian curvature of maximally symmetric spaces

  • center o bass
  • · Replies 3 ·
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3

Graduate Real Vector Space: Is Addition & Scalar Multiplication Smooth?

  • Geometry_dude
  • · Replies 4 ·
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4

Graduate Push Forward on a Product Manifold.

  • andresB
  • · Replies 4 ·
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4

Graduate Factor 1/2 in the Curvature Two-form of a Connection Principal Bundle

  • center o bass
  • · Replies 5 ·
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5

Graduate Extended plane as a topological sphere

  • TrickyDicky
  • · Replies 28 ·
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Graduate Contact Vector Fields. "Flow Preserves Contact Structure?

  • WWGD
  • · Replies 5 ·
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5

Graduate Can a k-Form Be Integrated Over Lower Dimensional Manifolds?

  • davi2686
  • · Replies 5 ·
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5

Graduate Why Is Cech Cohomology More Common Than Cech Homology?

  • WWGD
  • · Replies 3 ·
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3

Graduate Different types of differential geometry?

  • dyn
  • · Replies 13 ·
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13

A curvature problem (differentiation)

  • DreamWeaver
  • · Replies 2 ·
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Graduate Why only Closed Forms Matter in DeRham Cohomology?

  • WWGD
  • · Replies 7 ·
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7

Graduate How does metric give complete information about its space?

  • luinthoron
  • · Replies 11 ·
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11

Graduate Maurer-Cartan form involved in Lie bracket

  • center o bass
  • · Replies 4 ·
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4

Graduate Difference between mixed tensor notation

  • blankvin
  • · Replies 2 ·
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2

Undergrad Basic concepts about contra/covariance

  • davi2686
  • · Replies 17 ·
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17

Graduate Can I use generalized Stokes' theorem in Faraday's law?

  • davi2686
  • · Replies 12 ·
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12

Graduate Antisymmetric gradient matrix?

  • scoobmx
  • · Replies 1 ·
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1

High School Who Was Pavarotti's Understudy? What Are Second Order Tensors?

  • aditya ver.2.0
  • · Replies 11 ·
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11

Graduate The ant and honey problem on a spherical bowl - shortest paths?

  • nixed
  • · Replies 14 ·
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14

Graduate Curvature 1-forms in NP formalism

  • Quality Cheese
  • · Replies 2 ·
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2

Graduate What is the Definition of the Shape Operator and How is it Calculated?

  • Jhenrique
  • · Replies 7 ·
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7

Graduate Trivial Isometry Group for the Reals

  • Pond Dragon
  • · Replies 16 ·
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16

Graduate Intersection between rotated & translated ellipse and line

  • piercazzo
  • · Replies 1 ·
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Graduate How can I calculate a rotation using geometric algebra?

  • JonnyMaddox
  • · Replies 4 ·
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4

Graduate Does this spherical triangle exist?

  • nixed
  • · Replies 2 ·
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2

Graduate Coordinate free Christoffel symbols

  • kostas230
  • · Replies 15 ·
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15

Graduate Lie bracket of derivations in space of r-forms

  • Blazejr
  • · Replies 2 ·
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2

Graduate Can Vectors Only Associate Pseudo-Forms in Non-Cartesian Coordinates?

  • JonnyMaddox
  • · Replies 4 ·
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4

Graduate Area of a Sphere: Intuitive Problem Solved

  • ChrisVer
  • · Replies 4 ·
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4

Undergrad How to find all points along a great circle given two points on circle

  • fracs49er
  • · Replies 26 ·
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26

Graduate What is the difference b/w analytic, algebraic, differential geometry?

  • swampwiz
  • · Replies 15 ·
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15

Graduate Intersection between hyperplane within a simplex

  • Debashis
  • · Replies 3 ·
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3

Graduate Geometric Product: Definition and Calculation

  • JonnyMaddox
  • · Replies 5 ·
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5

Graduate Introducing K3 Manifold/Surface for Physicists

  • Lapidus
  • · Replies 2 ·
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2

Undergrad A Bit Confused About Polar Basis Vectors

  • MrBillyShears
  • · Replies 3 ·
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3

Graduate Confusion with Dot Product in Polar Coordinates with the Metric Tensor

  • MrBillyShears
  • · Replies 5 ·
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5

Graduate Lie derivative of contraction and of differential form

  • Blazejr
  • · Replies 5 ·
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5

Undergrad Modelling of a curve in 3D space

  • ann96
  • · Replies 2 ·
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Graduate 2-Plane Distribution in Cylindrical Coords.

  • WWGD
  • · Replies 3 ·
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Graduate Are Lie Groups with Identical Lie Algebras Always Homomorphic?

  • HomogenousCow
  • · Replies 2 ·
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Graduate Find radial imprint on rotating disk

  • HALON
  • · Replies 8 ·
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8

Graduate How Does the Kronecker Delta Lead to the Identity of Jacobians?

  • cr7einstein
  • · Replies 2 ·
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2

Graduate Average of Multiple Stress Tensors

  • phukanha
  • · Replies 1 ·
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1

Graduate Second derivative of a unit vector from The Feynman Lectures

  • ZetaOfThree
  • · Replies 1 ·
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1

Undergrad Only conservative vector fields are path independent?

  • princejan7
  • · Replies 2 ·
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2

Graduate Fields Medal 2014 to Maryam Mirzakhani

  • Astronuc
  • · Replies 1 ·
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1

Graduate Solve Hodge Star Operator Problem Step-by-Step

  • JonnyMaddox
  • · Replies 5 ·
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5

Explaining Isometries: Two Tasks

  • jljarrett18
  • · Replies 16 ·
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16

Graduate What is a Manifold? Curvature Explained in 3D Space

  • iyz
  • · Replies 12 ·
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12

Graduate What is the generalization of the tensor product definition for a three form?

  • JonnyMaddox
  • · Replies 10 ·
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10

Graduate Surface area of a Hypersphere?

  • shintashi
  • · Replies 4 ·
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4

Graduate Earth Geodesics - Rhumb Line vs Great Circle

  • GreenLRan
  • · Replies 6 ·
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6

Graduate Is the inner product of two rank n tensors a scalar?

  • 21joanna12
  • · Replies 4 ·
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4

Graduate Proof? Kronecker delta is the only isotropic second rank tensor

  • mSSM
  • · Replies 6 ·
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6

Graduate Path connected subgroups of SO(3),

  • Tinyboss
  • · Replies 3 ·
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3

Undergrad How Large Must a Circle Be for a Tangent to Cover an Area?

  • prashant.d000
  • · Replies 10 ·
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10

Graduate Does the Lie Bracket Always Close the Parallelogram as Described?

  • Pond Dragon
  • · Replies 1 ·
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1

Undergrad How Is the Surface Area of Spherical Cap Slices Calculated?

  • bobie
  • · Replies 9 ·
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9

Graduate How can the interior product be visualized using a concrete example?

  • JonnyMaddox
  • · Replies 11 ·
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11

Graduate Can Curvature Only Be Formed by Removing Sections of Flat Space?

  • friend
  • · Replies 9 ·
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9

Graduate Levi civita symbol and kronecker delta identities in 4 dimensions

  • Emil
  • · Replies 2 ·
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2

Graduate Can Principal Bundles Help with Lie Group Decomposition?

  • Pond Dragon
  • · Replies 1 ·
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1

Graduate The Geometry of Non-Euclidean Complex Planes

  • maline
  • · Replies 2 ·
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2

Graduate Which Computational Software Is Best for Tensorial Hermite Polynomials?

  • parulm
  • · Replies 3 ·
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3

Graduate Understanding 3D Rotations & Linear Relationships in Physics

  • electricspit
  • · Replies 2 ·
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2

Graduate Radius of Curvature: Formula & Name

  • manushanker20
  • · Replies 1 ·
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1

Undergrad What exactly is differential form?

  • quangtu123
  • · Replies 13 ·
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13

Calculating Radius of Circular Section from Sphere and Plane Intersection

  • marutkpadhy
  • · Replies 2 ·
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2

Graduate Computing geodesic distances from structural data

  • Munich
  • · Replies 1 ·
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1

Graduate Differential Form on Product Manifold

  • WWGD
  • · Replies 1 ·
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1

Graduate What kind of isometry? A metric tensor "respects" the foliation?

  • center o bass
  • · Replies 2 ·
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2

Graduate Foliation with isometric leaves.

  • center o bass
  • · Replies 3 ·
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3

Graduate Where is the uniqueness of smooth structure for involutive distributions proved?

  • center o bass
  • · Replies 1 ·
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1

Graduate Understanding F = ∇·F: The Relationship Between Scalar and Vector Fields

  • Jhenrique
  • · Replies 7 ·
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7

Undergrad 'Average Distance' Between Many Points

  • Nlc11
  • · Replies 9 ·
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9

Graduate Angle between two orthogonal coordinate systems

  • fannyfanfanz
  • · Replies 16 ·
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16

Graduate Geodesic Radius of Curvature Calculation Method

  • manushanker20
  • · Replies 2 ·
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2

Graduate Curl in 5D using levi-civita tensor

  • davi2686
  • · Replies 4 ·
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4

Graduate Maps of Ringed Spaces: Definition & Equivalence

  • Mandelbroth
  • · Replies 8 ·
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8

Graduate Indefinite Integrals of Scalar and Vector Fields: A Path Independence Dilemma?

  • Jhenrique
  • · Replies 12 ·
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12

Graduate Circle in the Complex Domain where Mean is not the Centre

  • electronicengi
  • · Replies 3 ·
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3

Surface Intersection: Paraboloid & Plane

  • evinda
  • · Replies 30 ·
2
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30

Graduate Understanding Scalar Fields: Tools for Studying Vector Field Behavior

  • Jhenrique
  • · Replies 7 ·
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7

Undergrad How can I scale the noise function in a 2D game map generator?

  • JohnLuck
  • · Replies 1 ·
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1

Undergrad What is the symmetry axis of a hyperbola and how can it be calculated?

  • Burger
  • · Replies 1 ·
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1

Graduate Products of Locally Ringed Spaces

  • Mandelbroth
  • · Replies 5 ·
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5

Graduate Area and volume integral of vector field

  • Jhenrique
  • · Replies 4 ·
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4

Graduate Vorticity and Flux of Vector Field ##\vec{f}## Explained

  • Jhenrique
  • · Replies 8 ·
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8

Undergrad Calculating the Radius of Curvature for a Deflected Beam

  • Jerry1989
  • · Replies 2 ·
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2

Undergrad Is it possible to convert 2D coordinates of point to 3D form ?

  • ramdas
  • · Replies 3 ·
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3

Graduate Question about Finsler geometry

  • Esmaeil
  • · Replies 1 ·
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1

Graduate Closed integration of exact form

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Geometric Interpretation of VSEPR Theory

  • Neolux
  • · Replies 3 ·
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3

Graduate Can Circulation be Computed in a System with an Open Path of Integration?

  • Jhenrique
  • · Replies 5 ·
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5

Graduate Is a Manifold Defined by Sheaves Always Hausdorff?

  • Mandelbroth
  • · Replies 3 ·
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3

Graduate Exploring the 3-Sphere: A Beginner's Guide to Higher Dimensions

  • Sunfire
  • · Replies 14 ·
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14

Graduate Why is grad(f) a covariant vector

  • Benjam:n
  • · Replies 2 ·
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2

Graduate Transformation behavior of the gradient

  • joda80
  • · Replies 2 ·
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2