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.
Find the point on a line that is X distance away from a plane
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Exploring Ansatz Metric of 4D Spacetime
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Geometrical interpretation of this coordinate transformation
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Christoffel Symbol Ansatz for 4D Spacetime
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Is There an Equation for a Rectangular Prism in Cartesian Coordinates?
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Integrable vs. Completely Integrable Distributions
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Find the point on a cone that is farthest in a given direction
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Constructing a chart with coord. basis equal to given basis at one pt.
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Why Are Homology Groups Not MUCH Larger?
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Are left-invariant fields mapped onto the manifold Killing vectors?
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Condition for a vector field be non-linear
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Solving Two Parabola Problems: Proving & Finding Values
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Vector fields, flows and tensor fields
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Geodesic equations and Christoffel symbols
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What are independent terms in Magnetic Tensor
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Tangent vector to curve - notational confusion.
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Killing vector field => global isomorphisms?
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Bounding General Shapes with Polygons, Especially Concave
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Questions on Orbifolds S^1/Z_2 and T^2/Z_2
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Recovering a frame field from its connection forms
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How Does the Restricted Three Body Problem Define Motion Manifolds?
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Connecting Lagrangian Density with Field Theory
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Is the Gradient of a Contravariant Vector a Covariant Vector?
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Problem about taking measurements in flat metric spaces
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Virtues of principal/associated bundle formulation of covariant deriv.
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Symmetrization of a tensor in spherical coordinate
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How to prove a vector bundle is non-trivial using transition functions
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Differentiation of coordinate wrt another coordinate
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Can Scalar Fields Be Decomposed into Symmetric and Antisymmetric Parts?
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Vector Derivatives Explained: Definition and Examples
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Circulation Definition: Understanding Positive, Null, and Negative Circulation
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Differential forms and differential operators
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Why Can Only Directional Derivatives Be Computed for Scalar Fields?
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Understanding Gradient and Curl: Equations and Directions
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Lagrangian Multipliers to find maximum and minimum values
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What is the relationship between Lie algebras and Lie groups on a manifold?
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Left-invariant vector field of the additive group of real number
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Diferentiation and differential operators
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Are all closed forms exact? Are all exact forms closed?
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Complete vector field X => X defined on the whole manifold?
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Generalized Helix: What Do You Think?
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Is Fibre Bundles Cartan's Generalization of Klein's Erlagen Program?
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The true TFC for surface integrals
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Curl in 2D is a vector or a scalar?
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Why are Lie Subgroups Defined as Immersed Submanifolds?
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How Can You Find the Inverse of the Exterior Derivative?
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Poor Phrasing of a Lie Group Theorem
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Derivations vs Directional derivatives
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Closed ball is manifold with boundary
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Finding the radius of a curved surface
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Originary Curves: Mathematical & Physical Properties
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Why Does the Constant Rank Theorem Hold True?
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Why is a Kähler form not always holomorphic?
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Cauchy Stress Tensor: Equilibrium Equations
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Metric and existence of parallel lines
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Geodesic curvature, normal curvature, and geodesic torsion
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Why Can't Polar Basis Vectors Be Defined as Unit Vectors?
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Solving Circle Equation with 2 Intersecting Vectors
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Connection between cesaro equation and polar coordinates
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2nd tangential angle and torsion
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Which is orientation of tangential angle in polar coordinates?
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Curvatures at Surface point for non-normal planes
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Is Complex Torsion the Key to Understanding Circular Helices Operations?
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R, dr and d²r and curvilinear coordinates
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What is the role of theta in representing polar vectors?
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Proving Stokes' Theorem for Beginners
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Group Cohomology: Borel's Finite & Lie Group Cases
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Existence of Hodge Dual: obvious or non-trivial?
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Understanding Laplacian's Theorem: A Comprehensive Guide
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Parallel transport around a loop
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Admitting Metric: Meaning & Explanation
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Charts on submersions (manifolds).
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Understanding Triply Periodic Surfaces: Translations and Invariance?
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What are the components of the vector d²r in relation to dr?
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Symmetry (killing vector) preserving diffeomorphisms
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Fundamental theorem of calculus for surface integrals?
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Yet more elementary questions about the tangent space
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Derivative of Unit Vector in a Rotating Frame
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Is it true that ##t=n\times b##?
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Formulating a Method of Steepest Ascent on Lie Groups
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Conditions for Solution to Pullback Equation on Forms?
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Example of a topological manifold without smooth transition functions.
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Program Computing Wedge of Differential Forms?
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Why Is My Covariant Derivative Result Incorrect?
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Is Local Flow of a Vector Field a Diffeomorphism?
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Understanding Derivatives of f(r) in Multiple Variables
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Smooth maps between manifolds domain restriction
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Are any two geodesics the same after applying an isometry?
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What Does Null-Homotopic Framing Mean in Knot Topology?
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How Do Different Coordinate Systems Affect Vector Operations?
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Metric tensor after constructing a quotient space.
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Deductions about extending a pseudo-riemannian manifold
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Top Homology of Connected , Orientable Manifolds with Boundary
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In how many ways can you embed a Riemannian manifold in R^n?
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Can Non-Smooth C^1 Knots be Orientable?
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Differential Geometry: Understanding the Affine Tangent Plane at a Point
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What Properties Are Preserved by Diffeomorphisms?
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How do axioms for Euclidean geometry exclude non-trivial topology?
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Orientation of a Submanifold, given an Orientation of Ambient Manifold
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Is the Dual of a Reeb field a Contact Form?
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