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 Question About Curvilinear Cooridnates
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Graduate Theory of Surfaces and Theory of Curves Relationship
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Undergrad How do I calculate the surface area of a rotated curve?
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Graduate Differential forms and vector calculus
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Undergrad Meaning of the sign of the geodesic curvature
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Graduate Interior products, exterior derivatives and one forms
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Undergrad Torsion on cylinder described differentially
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Graduate Torsion forms and particle physics
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Graduate Line integrals of differential forms
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Graduate Definition of the Lie derivative
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Graduate Square of the exterior derivative
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Graduate Ricci Form Notation: Need Help Understanding
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Graduate Action of a vector on the pull-back of a function
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Undergrad Make a Pseudo-Riemannian Metric Conformal
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Graduate Unique separation of the vertical and horizontal spaces?
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Undergrad (Index Notation) Summing a product of 3 numbers
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High School Trying to represent a written geometrical description
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Undergrad Levi-Civita: very small problem, need two steps explained
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Undergrad Confusion on Bianchi Identity proof
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Undergrad Lie derivative of a differential form
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Graduate Existence of Complex Structures and Characteristic Classes
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Graduate Maurer–Cartan forms for a matrix group?
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Graduate Tangent Bundle questions about commutative diagram
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Undergrad Conformal geometry vs. projective geometry
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Undergrad Questions about gradient and scalar product
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High School Base space Minkowski, fiber is S^1, total spaces?
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Undergrad Example of computing geodesics with 2D polar coordinates
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Undergrad (2,0) tensor is not a tensor product of two vectors?
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Graduate How Is the Taylor Expansion Applied to Metric Tensors?
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Undergrad Do derivative operators act on the manifold or in R^n?
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Graduate Question about Killing vector fields
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Graduate A question about coordinate distance & geometrical distance
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Undergrad Understanding the Transition Functions for S^1 Using Atlas Charts
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Undergrad Do Carmo's book, chap2 Regular surfaces, definition 1.2 -- question
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Graduate Question about Holonomy of metric connecton
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Undergrad Can there be a bounded space w/o a boundary w/o embedding?
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Undergrad Taylor expansion and parallel transport
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Graduate Confusion regarding conformal transformations
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Graduate Geometrical interpretation of Ricci and Riemann tensors?
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Undergrad Generalisation of Pythagoras theorem
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Graduate Transformation properties of the Christoffel symbols
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Undergrad Covariant and contravariat components
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Graduate Manifolds: local & global coordinate charts
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Undergrad Covariant derivative of a contravariant vector
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Graduate Difficulty in understanding contracted Bianchi identities
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Graduate Variation of Metrics: Formula & Proof Explained
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Undergrad Question about chart parameterization
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Undergrad Adjoint of the derivative in Minkowsky space.
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Undergrad Bounding the volume distortion of a manifold
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Undergrad Great Circle Distance Derivation
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Graduate Derive General Metric Wave Equation
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Undergrad Is the Tensor Product of Two Matrices Really This Simple?
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Graduate Expansion of covariant derivative
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Undergrad Curved space and curvilinear coordinates
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Graduate Riemann tensor and covariant derivative
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Graduate Non-Abelian Stokes theorem and variation of the EL action
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Graduate Möbius band diffrential geometry
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Undergrad Is that the definition of a lie group?
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Undergrad Observation of distances w.r.t. metric
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Graduate Normal velocity to the surface in Spherical Coordinate System
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Uniform grid of points on a sphere
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Graduate How can curl of 4-vector or 6-vector be writen?
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Graduate Continuous map from one manifold to another
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Graduate Integrating the topics of forms, manifolds, and algebra
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Graduate Is the Inner Product in Quaternionic Vector Spaces Truly Hyperhermitian?
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Undergrad The geometry of manifolds .... (an essay by R.O.Wells Jr.)
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Graduate Is the Dual Vector in Wald's Abstract Tensor Notation a Contraction?
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Graduate Differentiation of a product of 4-gradients wrt a 4-gradient
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Undergrad Infinitesimal area element in polar coordinate
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Undergrad 3D space curvature visualization
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Undergrad Difference between the projective space and one its part
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Graduate Ellipse of transformation from spherical to cartesian
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Graduate Field transformation under an active transformation
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Undergrad What is the scale factor in orthogonal vector calculus?
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Undergrad What Is the Genus of One-Dimensional Curves?
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Undergrad Prove what the exterior derivative of a 3-form is....
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Undergrad Is a Riemannian Metric Invariant Under Any Coordinate Transformation?
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Undergrad Velocity Vector Fields: Differentiating a Vector Function to Scalar
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Undergrad Are the Two Equations for Push-Forwards in Differential Geometry Equivalent?
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Undergrad Interior product with differential forms
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Graduate Is the Riemann Curvature Tensor a Mathematical Tool or Physically Significant?
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Undergrad Why are contravariant and covariant vectors important in general relativity?
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Graduate Weyl Tensor Gravity propagation
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Graduate Confusion on notion of connection & covariant derivative
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Graduate Can geodesic deviation be zero while curvature tensor is not
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Graduate Project img on X-Y surface to a cylinder placed in center....
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Undergrad Directional Derivatives and Derivations - Tangent Spaces
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Undergrad Shape defined by x∈ℂ^3 and x⋅x = 0.
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Graduate Derivative of smooth paths in Lie groups
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Undergrad Coordinates of Pushforwards .... General Case
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Pushforwards in local coordinates
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Computations with Tangent Vectors and Pushforwards - Lee
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Further Questions on Computations in Coordinates - Lee, Ch 3
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Maxwell's Equations in N Dimensions
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Example of transversal submanifolds?
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Prerequisites for non Euclidean geometry
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Definition of chart for Lie groups
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Manifolds - Charts on Real Projective Spaces
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Tensor product of two arbitrary vectors an arbitrary tensor?
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Tangent Spaces of Parametrized Sets - McInerney, Defn 3.3.5
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