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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Graduate Is Mean Curvature Invariant Under Coordinate Changes?
- WWGD
- · Replies 0 ·
Graduate Is every smooth simple closed curve a smooth embedding of the circle?
- Only a Mirage
- · Replies 8 ·
Undergrad Find the point on a line that is X distance away from a plane
- caibbor
- · Replies 6 ·
Undergrad Simple curve - not so simple function?
- Miffymycat
- · Replies 12 ·
Graduate Exploring Ansatz Metric of 4D Spacetime
- darida
- · Replies 3 ·
Graduate Geometrical interpretation of this coordinate transformation
- jam_27
- · Replies 6 ·
Graduate Christoffel Symbol Ansatz for 4D Spacetime
- darida
- · Replies 8 ·
High School Is There an Equation for a Rectangular Prism in Cartesian Coordinates?
- michael pranit
- · Replies 2 ·
Graduate Integrable vs. Completely Integrable Distributions
- center o bass
- · Replies 5 ·
Graduate Find the point on a cone that is farthest in a given direction
- caibbor
- · Replies 4 ·
Graduate Constructing a chart with coord. basis equal to given basis at one pt.
- center o bass
- · Replies 2 ·
Graduate Why Are Homology Groups Not MUCH Larger?
- Mandelbroth
- · Replies 3 ·
Graduate Are left-invariant fields mapped onto the manifold Killing vectors?
- center o bass
- · Replies 7 ·
Graduate Condition for a vector field be non-linear
- Jhenrique
- · Replies 3 ·
Graduate Solving Two Parabola Problems: Proving & Finding Values
- varunKanpur
- · Replies 3 ·
Graduate Vector fields, flows and tensor fields
- TrickyDicky
- · Replies 33 ·
Graduate Geodesic equations and Christoffel symbols
- Demon117
- · Replies 5 ·
Graduate What are independent terms in Magnetic Tensor
- welshrich
- · Replies 3 ·
Graduate Tangent vector to curve - notational confusion.
- center o bass
- · Replies 1 ·
Graduate Killing vector field => global isomorphisms?
- center o bass
- · Replies 8 ·
Graduate Bounding General Shapes with Polygons, Especially Concave
- downplay
- · Replies 1 ·
Graduate Questions on Orbifolds S^1/Z_2 and T^2/Z_2
- "pi"mp
- · Replies 1 ·
Graduate Recovering a frame field from its connection forms
- underflow
- · Replies 1 ·
Graduate How Does the Restricted Three Body Problem Define Motion Manifolds?
- baxter
- · Replies 1 ·
Graduate Connecting Lagrangian Density with Field Theory
- Geometry_dude
- · Replies 7 ·
Graduate Is the Gradient of a Contravariant Vector a Covariant Vector?
- nigelscott
- · Replies 2 ·
Graduate Problem about taking measurements in flat metric spaces
- haruna
- · Replies 2 ·
Graduate Virtues of principal/associated bundle formulation of covariant deriv.
- center o bass
- · Replies 1 ·
Graduate Why are Invariants so special?
- NoodleDurh
- · Replies 1 ·
Graduate Symmetrization of a tensor in spherical coordinate
- oliveriandrea
- · Replies 1 ·
Undergrad Curvature of a circle approaches zero as radius goes to infinity
- BOAS
- · Replies 5 ·
Graduate How to prove a vector bundle is non-trivial using transition functions
- nonequilibrium
- · Replies 2 ·
Undergrad Differentiation of coordinate wrt another coordinate
- Jhenrique
- · Replies 5 ·
Graduate Can Scalar Fields Be Decomposed into Symmetric and Antisymmetric Parts?
- Jhenrique
- · Replies 2 ·
Graduate Vector Derivatives Explained: Definition and Examples
- Jhenrique
- · Replies 11 ·
Graduate Circulation Definition: Understanding Positive, Null, and Negative Circulation
- Jhenrique
- · Replies 6 ·
Graduate Differential forms and differential operators
- Jhenrique
- · Replies 5 ·
Graduate Why Can Only Directional Derivatives Be Computed for Scalar Fields?
- Jhenrique
- · Replies 1 ·
Graduate Understanding Gradient and Curl: Equations and Directions
- Jhenrique
- · Replies 1 ·
Undergrad Lagrangian Multipliers to find maximum and minimum values
- cooev769
- · Replies 1 ·
Graduate What is the relationship between Lie algebras and Lie groups on a manifold?
- Matterwave
- · Replies 7 ·
Graduate Left-invariant vector field of the additive group of real number
- AlbertEi
- · Replies 2 ·
Graduate Is GL(n,C) the biggest complex manifold within GL(2n,R)?
- nonequilibrium
- · Replies 1 ·
Graduate Diferentiation and differential operators
- Jhenrique
- · Replies 7 ·
Graduate Are all closed forms exact? Are all exact forms closed?
- Jhenrique
- · Replies 4 ·
Axis Constrained Collision Distance
- dotails
- · Replies 1 ·
Graduate Complete vector field X => X defined on the whole manifold?
- center o bass
- · Replies 2 ·
Graduate Generalized Helix: What Do You Think?
- Abel Cavaşi
- · Replies 5 ·
Undergrad Finding a Function for a Family of Curves
- orthogonal
- · Replies 4 ·
Graduate Surface calculation (no integration)
- Jhenrique
- · Replies 7 ·
Graduate Is Fibre Bundles Cartan's Generalization of Klein's Erlagen Program?
- center o bass
- · Replies 1 ·
Graduate The true TFC for surface integrals
- Jhenrique
- · Replies 3 ·
Graduate Curl in 2D is a vector or a scalar?
- Jhenrique
- · Replies 5 ·
Graduate Why are Lie Subgroups Defined as Immersed Submanifolds?
- center o bass
- · Replies 3 ·
Graduate How Can You Find the Inverse of the Exterior Derivative?
- Jhenrique
- · Replies 1 ·
Graduate Poor Phrasing of a Lie Group Theorem
- Mandelbroth
- · Replies 1 ·
Graduate Derivations vs Directional derivatives
- center o bass
- · Replies 4 ·
Graduate Closed ball is manifold with boundary
- kostas230
- · Replies 2 ·
Graduate What is the mathematical concept behind the shear in gravitational lensing?
- zephyr5050
- · Replies 1 ·
Graduate Unit vectors in different coordinates
- JasonHathaway
- · Replies 1 ·
Undergrad Finding the radius of a curved surface
- mickeyc11
- · Replies 5 ·
Graduate Originary Curves: Mathematical & Physical Properties
- Abel Cavaşi
- · Replies 5 ·
Graduate Is the Modulus of a Tensor Calculated Differently Than a Vector?
- Jhenrique
- · Replies 1 ·
Graduate Why Does the Constant Rank Theorem Hold True?
- center o bass
- · Replies 1 ·
Graduate Why is a Kähler form not always holomorphic?
- nonequilibrium
- · Replies 14 ·
Graduate Cauchy Stress Tensor: Equilibrium Equations
- ARTjoMS
- · Replies 1 ·
Graduate Metric and existence of parallel lines
- ShayanJ
- · Replies 3 ·
Graduate Geodesic curvature, normal curvature, and geodesic torsion
- Demon117
- · Replies 6 ·
Graduate Why Can't Polar Basis Vectors Be Defined as Unit Vectors?
- epovo
- · Replies 1 ·
Undergrad Solving Circle Equation with 2 Intersecting Vectors
- pbayer123
- · Replies 1 ·
Undergrad Cross products for unit vectors in other coordinate systems
- AdkinsJr
- · Replies 4 ·
Graduate Connection between cesaro equation and polar coordinates
- Jhenrique
- · Replies 3 ·
Graduate 2nd tangential angle and torsion
- Jhenrique
- · Replies 3 ·
Undergrad Which is orientation of tangential angle in polar coordinates?
- Jhenrique
- · Replies 1 ·
Graduate Curvatures at Surface point for non-normal planes
- Soulagenda
- · Replies 15 ·
Graduate Is Complex Torsion the Key to Understanding Circular Helices Operations?
- Abel Cavaşi
- · Replies 2 ·
Graduate R, dr and d²r and curvilinear coordinates
- Jhenrique
- · Replies 5 ·
Graduate What is the role of theta in representing polar vectors?
- Gzyousikai
- · Replies 3 ·
Undergrad Proving Stokes' Theorem for Beginners
- Amsingh123
- · Replies 5 ·
Graduate Group Cohomology: Borel's Finite & Lie Group Cases
- electroweak
- · Replies 2 ·
Graduate Existence of Hodge Dual: obvious or non-trivial?
- nonequilibrium
- · Replies 1 ·
Graduate Understanding Laplacian's Theorem: A Comprehensive Guide
- Jhenrique
- · Replies 5 ·
Graduate Parallel transport around a loop
- dEdt
- · Replies 2 ·
Graduate Admitting Metric: Meaning & Explanation
- center o bass
- · Replies 3 ·
Graduate Charts on submersions (manifolds).
- center o bass
- · Replies 9 ·
Ernesto's question at Yahoo Answers regarding finding a locus of points
- MarkFL
- · Replies 1 ·
Graduate Understanding Triply Periodic Surfaces: Translations and Invariance?
- Demon117
- · Replies 1 ·
Graduate What are the components of the vector d²r in relation to dr?
- Jhenrique
- · Replies 8 ·
Graduate Symmetry (killing vector) preserving diffeomorphisms
- center o bass
- · Replies 1 ·
Undergrad Fundamental theorem of calculus for surface integrals?
- Jhenrique
- · Replies 9 ·
Graduate Yet more elementary questions about the tangent space
- orion
- · Replies 25 ·
Graduate Derivative of Unit Vector in a Rotating Frame
- Jhenrique
- · Replies 12 ·
Undergrad Is it true that ##t=n\times b##?
- DeadOriginal
- · Replies 1 ·
Graduate Formulating a Method of Steepest Ascent on Lie Groups
- Mandelbroth
- · Replies 3 ·
Graduate Conditions for Solution to Pullback Equation on Forms?
- WWGD
- · Replies 1 ·
Group Velocity and Phase Velocity
- Joystar77
- · Replies 1 ·
Graduate Example of a topological manifold without smooth transition functions.
- center o bass
- · Replies 15 ·
Graduate Program Computing Wedge of Differential Forms?
- WWGD
- · Replies 2 ·
Graduate Why Is My Covariant Derivative Result Incorrect?
- Jhenrique
- · Replies 1 ·
Graduate Is Local Flow of a Vector Field a Diffeomorphism?
- center o bass
- · Replies 1 ·