Differential Geometry And Mathematical Physics¶

4 domain-specific abstractions whose origin domain is Differential Geometry And Mathematical Physics.

Curvilinear coordinates — A locally invertible coordinate system on Euclidean space or a manifold whose coordinate curves or surfaces may be curved, with geometry represented through basis variation, metric coefficients and a Jacobian.
Mathai–Quillen formalism — Represent a vector bundle's Thom class by a canonical Gaussian differential form built with a connection and curvature, linking cohomological localization, superconnections and topological quantum field theory.
Orthogonal coordinates — A curvilinear coordinate system whose coordinate curves or hypersurfaces meet mutually at right angles, making the metric tensor diagonal in the coordinate basis.
Tensor field — A smoothly or otherwise regularly varying assignment of a tensor of fixed type to every point of a manifold or region.