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.
Undergrad Proving radial properties of particular dimensionless surface plots?
  • tade
  • · Replies 14 ·
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Graduate Equivalence of diffeomorphism definitions
  • Avatrin
  • · Replies 2 ·
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Graduate Logical foundations of smooth manifolds
  • Avatrin
  • · Replies 16 ·
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16
High School Are Polar Coordinates on ##\mathbb R^2## a Coordinate System?
  • kent davidge
  • · Replies 4 ·
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4
Undergrad Coordinate systems on the 2-sphere
  • kent davidge
  • · Replies 18 ·
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18
Tangent line to circle making 30º with a second circle
  • GONURVIA
  • · Replies 2 ·
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Graduate Second order partial derivatives vanish?
  • George Keeling
  • · Replies 3 ·
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3
Undergrad Finding the coordinates of a point on a sphere
  • lulukoko
  • · Replies 7 ·
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7
Graduate Question about covariant derivatives
  • George Keeling
  • · Replies 7 ·
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7
Undergrad Set of possible rotations of a 3D object and the rotation history
  • Spinnor
  • · Replies 40 ·
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Undergrad Is There a Generalized Fourier Transform for All Manifolds?
  • redtree
  • · Replies 1 ·
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Undergrad Deriving the spherical volume element
  • quickAndLucky
  • · Replies 3 ·
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3
Undergrad Spherical Harmonics Axisymmetry
  • Maher
  • · Replies 1 ·
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1
Graduate Variational derivative and Euler-Poincare equations
  • eipiplusone
  • · Replies 4 ·
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4
Graduate What is a differentiable variety?
  • Opressor
  • · Replies 1 ·
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1
Graduate How to calculate the matrix of a form?
  • Abhishek11235
  • · Replies 7 ·
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7
Graduate Pathological example of a Principle Fiber Bundle?
  • Geofleur
  • · Replies 11 ·
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11
Graduate Calculating Lie Derivative for Case (ii)
  • Abhishek11235
  • · Replies 4 ·
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4
Undergrad How to derive a symmetric tensor?
  • Cathr
  • · Replies 1 ·
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1
Undergrad Component derivative of a tensor
  • dsaun777
  • · Replies 10 ·
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10
Undergrad Tangent spaces at different points
  • kent davidge
  • · Replies 5 ·
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5
Undergrad Tangent vector basis and basis of coordinate chart
  • AndrewGRQTF
  • · Replies 6 ·
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6
High School Dimension of the metric of a projection of a sphere
  • jk22
  • · Replies 1 ·
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1
Undergrad Interpreting The Definition of Tensors
  • VuIcan
  • · Replies 6 ·
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6
Undergrad Tangent spaces at different points
  • kent davidge
  • · Replies 6 ·
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6
Undergrad Connections (principal bundles) ....
  • kent davidge
  • · Replies 3 ·
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3
Undergrad Understanding Differential Forms and Basis Vectors in Curved Space
  • kiuhnm
  • · Replies 24 ·
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24
Undergrad Are Coordinates on a Manifold Really Functions from R^n to R?
  • kiuhnm
  • · Replies 17 ·
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17
Undergrad Do index gymnastics change a tensor's dimensions?
  • snoopies622
  • · Replies 5 ·
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5
Undergrad Hopf fibration, stereoprojected fibers look close, can be?
  • Spinnor
  • · Replies 14 ·
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14
Graduate Definition of Tensor and.... Cotensor?
  • kiuhnm
  • · Replies 3 ·
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3
Undergrad What Does the $\star \sigma = 1$ Equation Reveal in Geometry?
  • kiuhnm
  • · Replies 6 ·
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Undergrad Gradient vector without a metric
  • kiuhnm
  • · Replies 17 ·
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17
Graduate Lie derivative of vector field defined through integral curv
  • Emil_M
  • · Replies 4 ·
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4
Graduate Invariance of Commutator Relations
  • fresh_42
  • · Replies 2 ·
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2
Undergrad How Are Basis Vectors Defined in Different Coordinate Systems?
  • olgerm
  • · Replies 14 ·
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14
Undergrad Covariant Derivatives: Doubt on Jolt & Proving Zj Γjk Vi = 0
  • kiuhnm
  • · Replies 11 ·
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Undergrad Christoffel symbol ("undotting")
  • kiuhnm
  • · Replies 3 ·
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3
Graduate Is there any tensor that gives the radius of a sphere?
  • cozycoz
  • · Replies 1 ·
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1
Undergrad Injective immersion that is not a smooth embedding
  • cianfa72
  • · Replies 7 ·
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7
High School Problem about a cone and plane cutting it
  • Julio
  • · Replies 14 ·
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14
Undergrad Differential structure on a half-cone
  • cianfa72
  • · Replies 9 ·
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9
Graduate Intrinsic definition on a manifold
  • kiuhnm
  • · Replies 9 ·
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9
Graduate Fundamental definition of extrinsic curvature
  • PLuz
  • · Replies 3 ·
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3
High School Confusion about the radius unit vector in spherical coordinates
  • random_soldier
  • · Replies 7 ·
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7
Undergrad Why vector lengths may not be preserved?
  • Nusc
  • · Replies 7 ·
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7
High School Differentiable function - definition on a manifold
  • cianfa72
  • · Replies 2 ·
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2
Graduate Pullback of F on Manifolds: What Matrix Do We Take Determinant Of?
  • Rico1990
  • · Replies 2 ·
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Undergrad About the properties of the Divergence of a vector field
  • aboutammam
  • · Replies 1 ·
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1
Graduate Is the Wedge Product of a 0-Form and l-Form Equal to f * η?
  • Maxi1995
  • · Replies 4 ·
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Graduate Differentiability of a function between manifolds
  • Maxi1995
  • · Replies 3 ·
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3
Graduate How Does the Chain Rule Define the Differential of a Function on a Manifold?
  • Maxi1995
  • · Replies 4 ·
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4
Undergrad Why is the Alternator Alternating?
  • Maxi1995
  • · Replies 2 ·
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Undergrad Rotating Coordinates: Solving for x and y
  • Nusc
  • · Replies 4 ·
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4
Undergrad Differential of the coordinate functions
  • Rico1990
  • · Replies 1 ·
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Graduate How do I pass a magnetic field to any coordinate system?
  • raistlin
  • · Replies 4 ·
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4
Graduate Coefficients in the linear combination of a k-form
  • Maxi1995
  • · Replies 6 ·
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Graduate Defining a Contact Structure Globally -- Obstructions?
  • WWGD
  • · Replies 5 ·
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Undergrad Difference between vectors and one-forms
  • Silviu
  • · Replies 25 ·
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Graduate Hessian as "Square" of Jacobian?
  • WWGD
  • · Replies 1 ·
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Undergrad Showing that the image of an arbitrary patch is an open set
  • Gene Naden
  • · Replies 7 ·
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7
Undergrad Do Isometries Preserve Covariant Derivatives?
  • Gene Naden
  • · Replies 14 ·
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Undergrad Differential for surface of revolution
  • Gene Naden
  • · Replies 30 ·
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Volume of $E$ in $\mathbb{R}^4$ - AMM
  • MountEvariste
  • · Replies 1 ·
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Graduate The Distance between two points in a hypothetical universe
  • DAirey
  • · Replies 1 ·
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1
Undergrad Connection forms and dual 1-forms for cylindrical coordinate
  • Gene Naden
  • · Replies 3 ·
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3
Undergrad Christoffel symbol and Einstein summation convention
  • Mathematicsresear
  • · Replies 1 ·
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1
Undergrad Riemann Tensor knowing Christoffel symbols (check my result)
  • Confused Physicist
  • · Replies 17 ·
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17
Undergrad How Is the Exponential Map Defined for Lie Groups Without a Metric?
  • wacki
  • · Replies 3 ·
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3
Graduate Computing de Rham Cohomology of Connected Sums of Objects
  • Calabi
  • · Replies 13 ·
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13
Find Angles of Spherical Triangle $\mathcal{P}$
  • Rorschach
  • · Replies 1 ·
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1
Undergrad Christoffel symbols knowing Line Element (check my result)
  • Confused Physicist
  • · Replies 6 ·
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6
Graduate Penrose paragraph on Bundle Cross-section?
  • Abhishek11235
  • · Replies 15 ·
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15
Undergrad Problem: perturbation of Ricci tensor
  • dpopchev
  • · Replies 3 ·
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3
High School Proving Linearity in Coordinate Transformation: A Mathematical Approach
  • shahbaznihal
  • · Replies 6 ·
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6
Undergrad More elegant way to solve divergence of arbitrary dotproduct
  • maxknrd
  • · Replies 9 ·
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9
Undergrad What is the proof that the divergence is normal to the surface?
  • swampwiz
  • · Replies 6 ·
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Undergrad Lie derivative of a metric determinant
  • Frank Castle
  • · Replies 20 ·
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Undergrad How to write the Frenet equations using the vector gradient?
  • HaniZaheer
  • · Replies 9 ·
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9
Graduate Possible Error in Vladimir Arnold Mathematical Methods C
  • xdrgnh
  • · Replies 4 ·
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4
High School How Many Parameters Are Needed to Parametrize the 3-Sphere?
  • jk22
  • · Replies 19 ·
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19
Undergrad Examples of Non-Orthogonal Curvilinear Coordinates
  • Frank Peters
  • · Replies 7 ·
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7
Graduate Is Every Smoothly Extendable Submanifold Properly Embedded?
  • JYM
  • · Replies 13 ·
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13
Graduate Finding the unit Normal to a surface using the metric tensor.
  • Abhishek11235
  • · Replies 3 ·
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Graduate Constructing a sequence in a manifold
  • JYM
  • · Replies 1 ·
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Undergrad What is the Formula for Computing Surface Metric on a PF Surface?
  • member 428835
  • · Replies 2 ·
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Undergrad What is the magnitude of a tensor?
  • granzer
  • · Replies 9 ·
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9
Undergrad Computation of the left invariant vector field for SO(3)
  • nigelscott
  • · Replies 1 ·
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Undergrad Meaning of cross terms in line element
  • beefbrisket
  • · Replies 1 ·
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1
Graduate Connection 1-forms to Christoffel symbols
  • WendysRules
  • · Replies 5 ·
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Graduate Explicit examples of calculations of Chern classes
  • nrqed
  • · Replies 22 ·
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Graduate Family of curves tangent to a smooth distribution of lines
  • Lodeg
  • · Replies 5 ·
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Graduate [Diff Forms & Skyrmions] What is this called?
  • vsv86
  • · Replies 3 ·
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3
Undergrad Some Questions on Differential Forms and Their Meaningfulness
  • jedishrfu
  • · Replies 28 ·
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High School A question about Gauss' Theorem
  • Wrichik Basu
  • · Replies 2 ·
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Graduate Coordinate representation of a diffeomorphism
  • stevendaryl
  • · Replies 4 ·
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4
Undergrad Is the Proof of Statement (3) in Lipschultz's Differential Geometry Justifiable?
  • facenian
  • · Replies 9 ·
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Undergrad What is the covariant derivative of the position vector?
  • Alain De Vos
  • · Replies 6 ·
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6
Undergrad Metrics & Topologies: Do Different Metrics Induce Different Topologies?
  • kent davidge
  • · Replies 9 ·
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Graduate Smoothness of multivariable function
  • JYM
  • · Replies 2 ·
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