Differential Geometry Forum

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Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
How to know if plane is perpendicular to another plane?
  • nicole1
  • · Replies 2 ·
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2
What Is the Distance Between Lines HO and PB in a Cuboid?
  • Monoxdifly
  • · Replies 2 ·
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2
Graduate Can Smooth Functions be Extended on Manifolds?
  • JYM
  • · Replies 10 ·
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10
Undergrad Is the Boundary Chart for a Closed Unit Ball Injective?
  • JYM
  • · Replies 2 ·
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2
Graduate Question About Elementary Fiber Bundle Example
  • Ghost Repeater
  • · Replies 6 ·
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6
Angle between line and the axis
  • karthikS
  • · Replies 4 ·
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4
High School Why Does Vqp Need to be Tangential to Vq in Order for Q to Get Closest to P?
  • Jas
  • · Replies 5 ·
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5
Undergrad Does a covariant version of Euler-Lagrange exist?
  • JuanC97
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2
Undergrad Basic Q about Vector/tensor definition and velocity
  • Gadhav
  • · Replies 11 ·
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11
Graduate What Is the Purpose of Exterior Forms in Differential Geometry?
  • phoenix95
  • · Replies 5 ·
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5
Undergrad Coherent operations on Jacobian matrices
  • Mapprehension
  • · Replies 2 ·
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2
Undergrad Connections on principal bundles
  • Silviu
  • · Replies 1 ·
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1
Graduate Pushforward of Smooth Vector Fields
  • Zag
  • · Replies 1 ·
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1
Cos^2(∠POA)+cos^2(∠POB)+cos^2(∠POC)+cos^2(∠POD) is independent of P.
  • lfdahl
  • · Replies 2 ·
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2
Calculating Coordinates of Spherical Triangles
  • Kel1980
  • · Replies 7 ·
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7
Undergrad Demo of cosine direction with curvilinear coordinates
  • fab13
  • · Replies 16 ·
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16
Undergrad On the Gaussian Curvature of time-like surfaces
  • deRoy
  • · Replies 2 ·
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2
What is the Maximum Inclination of a 3D Plane and its Equation in the XY Plane?
  • cptolemy
  • · Replies 1 ·
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1
Undergrad Understanding Fibre Bundles: A Layman's Guide
  • Silviu
  • · Replies 7 ·
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7
Graduate Characterizing the adjoint representation
  • Luck0
  • · Replies 3 ·
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3
Graduate How do dual vectors and tangent bases relate in coordinate functions?
  • nigelscott
  • · Replies 3 ·
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3
Graduate Diagonalization of adjoint representation of a Lie Group
  • Luck0
  • · Replies 4 ·
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4
High School Any geometrical meaning of multiplication of quaternions?
  • Kumar8434
  • · Replies 3 ·
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3
Translation Surfaces: Geometric Definition & Billiard Systems
  • Joppy
  • · Replies 4 ·
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4
Undergrad Deduce Geodesics equation from Euler equations
  • fab13
  • · Replies 5 ·
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5
Undergrad Coordinate systems vs. Euclidean space
  • JTC
  • · Replies 9 ·
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9
Graduate Is tangent bundle TM the product manifold of M and T_pM?
  • Joker93
  • · Replies 55 ·
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Undergrad Covariant derivative of Ricci scalar causing me grief
  • ft_c
  • · Replies 4 ·
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4
Formula for changing a plane intersection angle
  • LMHmedchem
  • · Replies 3 ·
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3
High School Ellipse tangent line using projections
  • arthur werbrouck
  • · Replies 1 ·
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1
High School Prove that tangents to the focal cord of parabola....
  • Vriska
  • · Replies 8 ·
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8
Undergrad How is the Index Raised or Lowered on a Conformally Related Metric?
  • Silviu
  • · Replies 4 ·
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4
Undergrad Why does a parallelizable manifold imply zero Riemann tensor?
  • Silviu
  • · Replies 6 ·
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6
Undergrad Surface area of inner and outer halves of torus
  • TheCanadian
  • · Replies 7 ·
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7
Undergrad Understanding Kunneth Formula and Tensor Product in r-Forms
  • Silviu
  • · Replies 2 ·
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2
Undergrad How Does Nakahara Compactify I=[0,1] to S^1 in De Rham Cohomology Proof?
  • Silviu
  • · Replies 11 ·
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11
Undergrad Understanding ##SO(2)## as Isotropy Group for ##x \in R^3##
  • Silviu
  • · Replies 3 ·
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3
Undergrad Understanding the Wedge Product on a 3-dim Manifold
  • Silviu
  • · Replies 7 ·
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7
High School What is the definition of a straight line in mathematics?
  • Lunct
  • · Replies 7 ·
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7
Graduate On the dependence of the curvature tensor on the metric
  • Joker93
  • · Replies 6 ·
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6
Undergrad Maurer-Cartan Form: Is it a One Form?
  • Silviu
  • · Replies 5 ·
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5
Graduate Can you give an example of a non-Levi Civita connection?
  • Joker93
  • · Replies 10 ·
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10
Undergrad Arbitrariness of connection and arrow on sphere
  • strauser
  • · Replies 14 ·
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14
Graduate Can I change topology of the physical system smoothly?
  • lichen1983312
  • · Replies 3 ·
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3
Graduate Integration along a loop in the base space of U(1) bundles
  • lichen1983312
  • · Replies 12 ·
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12
Undergrad Differential geometry in physics
  • Silviu
  • · Replies 1 ·
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1
Graduate Which Mathematicians are focused on Hodge Conjecture?
  • Allehujah
  • · Replies 1 ·
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1
Undergrad Understanding De Rham's Period and Stokes Theorem
  • Silviu
  • · Replies 5 ·
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5
Graduate Product of 3rd rank tensor with squared vector
  • SchroedingersLion
  • · Replies 9 ·
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9
High School Eliminating Variables in Trigonometric Equations for Research Purposes
  • highflyyer
  • · Replies 4 ·
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4
Graduate Can I find a smooth vector field on the patches of a torus?
  • lichen1983312
  • · Replies 4 ·
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4
Undergrad Coordinate transformation - Rotation
  • Quanta
  • · Replies 10 ·
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10
Undergrad Convert from rectangular to Spherical Coordinates
  • Philosophaie
  • · Replies 33 ·
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Graduate Find a circle inside of and tangent to a larger circle
  • Ventrella
  • · Replies 23 ·
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Graduate What's the Proper Way to Push Forward a Vector Field in Differential Geometry?
  • kiuhnm
  • · Replies 5 ·
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5
Undergrad Left translate back to I in SO(3)
  • JTC
  • · Replies 6 ·
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6
Undergrad Calculate object distance by using just the parallax angles
  • jay t
  • · Replies 15 ·
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15
Undergrad Is this 4-Vector cross product calculation correct?
  • Philosophaie
  • · Replies 6 ·
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6
Graduate Proving the Differential Map (Pushforward) is Well-Defined
  • Fgard
  • · Replies 4 ·
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4
Graduate Need (or not) for invoking axiom of choice in a certain case
  • RockyMarciano
  • · Replies 69 ·
3
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Graduate Covariant derivative only for tensor
  • mertcan
  • · Replies 3 ·
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3
Undergrad Is the Lorentz group non-compact?
  • Silviu
  • · Replies 7 ·
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7
Undergrad Understanding Integration on an Orientable Manifold
  • Silviu
  • · Replies 1 ·
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1
Graduate Compact Lie Group: Proof of Discrete Center & Finite Size?
  • Calabi
  • · Replies 14 ·
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14
Undergrad Interior Product: Definition & Understanding
  • Silviu
  • · Replies 2 ·
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2
Undergrad How Can Wedge Products Be Used in Differential Geometry?
  • Silviu
  • · Replies 2 ·
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2
Undergrad Why Is the Lie Bracket a Vector Field on a Manifold?
  • Silviu
  • · Replies 4 ·
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4
Graduate Christoffel symbols expansion for second derivatives
  • mertcan
  • · Replies 10 ·
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10
Undergrad What are the components of a vector field on a manifold?
  • Silviu
  • · Replies 4 ·
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4
The Fonz's Struggle with Geometry: Henry Winkler's Candid Confessions
  • mathdad
  • · Replies 5 ·
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5
Graduate Split the differential and differential forms
  • JTC
  • · Replies 2 ·
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2
Undergrad Problems in Differential geometry
  • Silviu
  • · Replies 1 ·
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1
Graduate Understanding Metric Tensor Calculations for Different Coordinate Systems
  • JTC
  • · Replies 10 ·
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10
Finding missing point of a vector when it is perpendicular to a line
  • AJTheRed
  • · Replies 2 ·
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2
Graduate Understanding the Dual Basis and Its Directions
  • JTC
  • · Replies 9 ·
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9
Undergrad Transformation of covariant vector components
  • saadhusayn
  • · Replies 1 ·
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1
Undergrad Hyperbolic space simulation in VR
  • VladZH
  • · Replies 2 ·
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2
Undergrad Extrinsic Curvature Formulas in General Relativity: Are They Equivalent?
  • craigthone
  • · Replies 4 ·
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4
Undergrad Question about Haar measures on lie groups
  • Luck0
  • · Replies 4 ·
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4
Distance between point and line
  • Yankel
  • · Replies 1 ·
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1
Graduate Examples of application of transversality of submanifolds
  • aboutammam
  • · Replies 1 ·
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1
Undergrad Finding Killing Vectors for $$ds^2 = dr^2 + r^2d\theta^2$$
  • davidge
  • · Replies 14 ·
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14
Undergrad Volumes of n-Spheres: Intuition & Calculations
  • martix
  • · Replies 8 ·
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8
Graduate Intution behind the definition of extrinsic curvature
  • Afonso Campos
  • · Replies 2 ·
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2
Undergrad Why Does the Area Element Vanish at the Origin in Polar Coordinates?
  • davidge
  • · Replies 24 ·
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24
Graduate Why Does Frankel Prefer Components on the Right in The Geometry of Physics?
  • JTC
  • · Replies 7 ·
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7
Undergrad Coordinate Charts: Clarifying Misunderstanding
  • ConfusedMonkey
  • · Replies 7 ·
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7
Undergrad Clifford Algebra and its contributions to physics
  • Phylosopher
  • · Replies 11 ·
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11
Graduate Streamlines from strain rate tensor
  • vktsn0303
  • · Replies 2 ·
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2
Undergrad Coordinate system vs ordered basis
  • ConfusedMonkey
  • · Replies 7 ·
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7
Undergrad Is My Understanding of the Generalized Stokes' Theorem Correct?
  • davidge
  • · Replies 1 ·
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1
Undergrad Product rule for exterior covariant derivative
  • Physics_Stuff
  • · Replies 2 ·
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2
Undergrad Understanding Parallel Transport
  • Arcturus7
  • · Replies 9 ·
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9
Undergrad Metric tensor derived from a geodesic
  • VladZH
  • · Replies 9 ·
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9
Graduate Is Your Graph Homeomorphic to a Sphere?
  • kroni
  • · Replies 3 ·
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3
High School Achieving Rotational Symmetry with Tetrahedral Universal Joints
  • DaveC426913
  • · Replies 11 ·
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11
Graduate LeviCivita in Orthogonal Curvilinear Coordinate System: "Cross Product Matrix
  • ltkach2015
  • · Replies 2 ·
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2
Graduate Curvature of Flat Lorentz manifolds
  • lavinia
  • · Replies 31 ·
2
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31
Undergrad Whats the meaning of Parallel in Vectors
  • Arman777
  • · Replies 7 ·
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7
Graduate About Chern number of U(1) principal bundle on a torus
  • lichen1983312
  • · Replies 28 ·
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28