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