Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
Threads
Graduate Smoothness of multivariable function
- JYM
- · Replies 2 ·
Vector equation of a plane perpendicular to the z axis
- nicole1
- · Replies 2 ·
What Is the Distance Between Lines HO and PB in a Cuboid?
- Monoxdifly
- · Replies 2 ·
Graduate Can Smooth Functions be Extended on Manifolds?
- JYM
- · Replies 10 ·
Undergrad Is the Boundary Chart for a Closed Unit Ball Injective?
- JYM
- · Replies 2 ·
Graduate Trivial vs non-trivial fiber bundles in Nakahara example 9.1
- Ghost Repeater
- · Replies 6 ·
Angle between line and the axis
- karthikS
- · Replies 4 ·
High School Why Does Vqp Need to be Tangential to Vq in Order for Q to Get Closest to P?
- Jas
- · Replies 5 ·
Undergrad Does a covariant version of Euler-Lagrange exist?
- JuanC97
- · Replies 2 ·
Undergrad Basic Q about Vector/tensor definition and velocity
- Gadhav
- · Replies 11 ·
Graduate What Is the Purpose of Exterior Forms in Differential Geometry?
- phoenix95
- · Replies 5 ·
Undergrad Coherent operations on Jacobian matrices
- Mapprehension
- · Replies 2 ·
Undergrad Connections on principal bundles
- Silviu
- · Replies 1 ·
Graduate Pushforward of Smooth Vector Fields
- Zag
- · Replies 1 ·
Cos^2(∠POA)+cos^2(∠POB)+cos^2(∠POC)+cos^2(∠POD) is independent of P.
- lfdahl
- · Replies 2 ·
Calculating Coordinates of Spherical Triangles
- Kel1980
- · Replies 7 ·
Undergrad Demo of cosine direction with curvilinear coordinates
- fab13
- · Replies 16 ·
Undergrad On the Gaussian Curvature of time-like surfaces
- deRoy
- · Replies 2 ·
What is the Maximum Inclination of a 3D Plane and its Equation in the XY Plane?
- cptolemy
- · Replies 1 ·
Undergrad What exactly is a fibre bundle and how should I visualize it?
- Silviu
- · Replies 7 ·
Graduate Characterizing the adjoint representation
- Luck0
- · Replies 3 ·
Graduate How do dual vectors and tangent bases relate in coordinate functions?
- nigelscott
- · Replies 3 ·
Graduate Diagonalization of adjoint representation of a Lie Group
- Luck0
- · Replies 4 ·
High School Any geometrical meaning of multiplication of quaternions?
- Kumar8434
- · Replies 3 ·
Non-convex polygons in translation surface definitions
- Joppy
- · Replies 4 ·
Undergrad Deduce Geodesics equation from Euler equations
- fab13
- · Replies 5 ·
Undergrad Coordinate systems vs. Euclidean space
- JTC
- · Replies 9 ·
Graduate Is tangent bundle TM the product manifold of M and T_pM?
- Joker93
- · Replies 55 ·
Undergrad Covariant derivative of Ricci scalar causing me grief
- ft_c
- · Replies 4 ·
Formula for changing a plane intersection angle
- LMHmedchem
- · Replies 3 ·
High School Ellipse tangent line using projections
- arthur werbrouck
- · Replies 1 ·
High School Tangents to focal chord of parabola perpendicular via reflection property
- Vriska
- · Replies 8 ·
Undergrad How is the Index Raised or Lowered on a Conformally Related Metric?
- Silviu
- · Replies 4 ·
Undergrad Why does a parallelizable manifold imply zero Riemann tensor?
- Silviu
- · Replies 6 ·
Undergrad Surface area of inner and outer halves of torus
- TheCanadian
- · Replies 7 ·
Undergrad Understanding Kunneth Formula and Tensor Product in r-Forms
- Silviu
- · Replies 2 ·
Undergrad How Does Nakahara Compactify I=[0,1] to S^1 in De Rham Cohomology Proof?
- Silviu
- · Replies 11 ·
Undergrad Understanding ##SO(2)## as Isotropy Group for ##x \in R^3##
- Silviu
- · Replies 3 ·
Undergrad Wedge product of cohomology classes on a 3-dimensional manifold
- Silviu
- · Replies 7 ·
High School What is the definition of a straight line in mathematics?
- Lunct
- · Replies 7 ·
Graduate On the dependence of the curvature tensor on the metric
- Joker93
- · Replies 6 ·
Undergrad Maurer-Cartan Form: Is it a One Form?
- Silviu
- · Replies 5 ·
Graduate Can you give an example of a non-Levi Civita connection?
- Joker93
- · Replies 10 ·
Undergrad Arbitrariness of connection and arrow on sphere
- strauser
- · Replies 14 ·
Graduate Can I change topology of the physical system smoothly?
- lichen1983312
- · Replies 3 ·
Graduate Integration along a loop in the base space of U(1) bundles
- lichen1983312
- · Replies 12 ·
Undergrad Using differential geometry to gain new insights in classical physics
- Silviu
- · Replies 1 ·
Graduate Which Mathematicians are focused on Hodge Conjecture?
- Allehujah
- · Replies 1 ·
Undergrad Understanding De Rham's Period and Stokes Theorem
- Silviu
- · Replies 5 ·
Graduate Product of 3rd rank tensor with squared vector
- SchroedingersLion
- · Replies 9 ·
High School Eliminating Variables in Trigonometric Equations for Research Purposes
- highflyyer
- · Replies 4 ·
Graduate Can I find a smooth vector field on the patches of a torus?
- lichen1983312
- · Replies 4 ·
Undergrad Coordinate transformation - Rotation
- Quanta
- · Replies 10 ·
Undergrad Convert from rectangular to Spherical Coordinates
- Philosophaie
- · Replies 33 ·
Graduate Find a circle inside of and tangent to a larger circle
- Ventrella
- · Replies 23 ·
Graduate What's the Proper Way to Push Forward a Vector Field in Differential Geometry?
- kiuhnm
- · Replies 5 ·
Undergrad Left translate back to I in SO(3)
- JTC
- · Replies 6 ·
Undergrad Calculate object distance by using just the parallax angles
- jay t
- · Replies 15 ·
Undergrad Is this 4-Vector cross product calculation correct?
- Philosophaie
- · Replies 6 ·
Graduate Proving the Differential Map (Pushforward) is Well-Defined
- Fgard
- · Replies 4 ·
Graduate Need (or not) for invoking axiom of choice in a certain case
- RockyMarciano
- · Replies 69 ·
Graduate Covariant derivative only for tensor
- mertcan
- · Replies 3 ·
Undergrad Is the Lorentz group non-compact?
- Silviu
- · Replies 7 ·
Undergrad Understanding Integration on an Orientable Manifold
- Silviu
- · Replies 1 ·
Graduate Why is G compact if Ad(G) is compact and Z(G) discrete?
- Calabi
- · Replies 14 ·
Undergrad Interior product: why does contraction reduce the degree?
- Silviu
- · Replies 2 ·
Undergrad How Can Wedge Products Be Used in Differential Geometry?
- Silviu
- · Replies 2 ·
Undergrad Why Is the Lie Bracket a Vector Field on a Manifold?
- Silviu
- · Replies 4 ·
Graduate Christoffel symbols expansion for second derivatives
- mertcan
- · Replies 10 ·
Undergrad What are the components of a vector field on a manifold?
- Silviu
- · Replies 4 ·
The Fonz's Struggle with Geometry: Henry Winkler's Candid Confessions
- mathdad
- · Replies 5 ·
Graduate Split the differential and differential forms
- JTC
- · Replies 2 ·
Undergrad Problems in Differential geometry
- Silviu
- · Replies 1 ·
Graduate Understanding Metric Tensor Calculations for Different Coordinate Systems
- JTC
- · Replies 10 ·
Finding missing point of a vector when it is perpendicular to a line
- AJTheRed
- · Replies 2 ·
Graduate Why can't I visualize directions of dual basis vectors dx^i?
- JTC
- · Replies 9 ·
Undergrad Transformation of covariant vector components
- saadhusayn
- · Replies 1 ·
Undergrad Hyperbolic space simulation in VR
- VladZH
- · Replies 2 ·
Undergrad Extrinsic Curvature Formulas in General Relativity: Are They Equivalent?
- craigthone
- · Replies 4 ·
Undergrad Does the Haar measure change when switching representations on a Lie group?
- Luck0
- · Replies 4 ·
Distance between point and line
- Yankel
- · Replies 1 ·
Graduate Examples of application of transversality of submanifolds
- aboutammam
- · Replies 1 ·
Undergrad Finding Killing Vectors for $$ds^2 = dr^2 + r^2d\theta^2$$
- davidge
- · Replies 14 ·
Undergrad Slicing n-spheres to find 3D volumes in 4D space
- martix
- · Replies 8 ·
Graduate Why is extrinsic curvature defined as the Lie derivative of the induced metric?
- Afonso Campos
- · Replies 2 ·
Undergrad Why Does the Area Element Vanish at the Origin in Polar Coordinates?
- davidge
- · Replies 24 ·
Graduate Why Does Frankel Prefer Components on the Right in The Geometry of Physics?
- JTC
- · Replies 7 ·
Undergrad Coordinate Charts: Clarifying Misunderstanding
- ConfusedMonkey
- · Replies 7 ·
Undergrad Clifford Algebra and its contributions to physics
- Phylosopher
- · Replies 11 ·
Graduate Streamlines from strain rate tensor
- vktsn0303
- · Replies 2 ·
Undergrad Coordinate system vs ordered basis
- ConfusedMonkey
- · Replies 7 ·
Undergrad Is My Understanding of the Generalized Stokes' Theorem Correct?
- davidge
- · Replies 1 ·
Undergrad Product rule for exterior covariant derivative
- Physics_Stuff
- · Replies 2 ·
Undergrad Understanding Parallel Transport
- Arcturus7
- · Replies 9 ·
Undergrad Metric tensor derived from a geodesic
- VladZH
- · Replies 9 ·
Graduate Is Your Graph Homeomorphic to a Sphere?
- kroni
- · Replies 3 ·
High School Achieving Rotational Symmetry with Tetrahedral Universal Joints
- DaveC426913
- · Replies 11 ·
Graduate LeviCivita in Orthogonal Curvilinear Coordinate System: "Cross Product Matrix
- ltkach2015
- · Replies 2 ·
Graduate Curvature of Flat Lorentz manifolds
- lavinia
- · Replies 31 ·
Undergrad Whats the meaning of Parallel in Vectors
- Arman777
- · Replies 7 ·