Connection (mathematics)

in Riemannian geometry, the coefficient of the Levi-Civita connection of a Riemannian metric

in differential geometry, a map between two fibres of a fibre bundle induced by a path between the points in the path space connecting the two fibres and a connection in the fibre bundle

specification of derivatives along tangent vectors of a manifold

geometrical idea of transporting data along a curve or family of curves in a parallel and consistent manner

mathematical theory in which noncommutative algebraic structures are interpreted as rings of functions on an abstract space

construct allowing differentiation of tangent vector fields of manifolds

the unique torsion-free affine connection that preserves a given (pseudo-)Rimannian metric

(1,2)-tensor field associated to an affine connection; characterizes "twist" of geodesics; if nonzero, geodesics will be helices

alt=Visualisation of parallel transport on a sphere|thumb|Parallel transport on a sphere along a piecewise smooth path. The initial vector is labelled as V, parallel transported along the curve, and the resulting vector is labelled as \mathcal{P}_{\gamma}(V). The outcome of parallel transport will be different if the path is varied.

math/physics concept

unique existence of the Levi-Civita connection

linear connection on a vector bundle

generalization of affine connections

Ehresmann connection on a principal bundle that is compatible with the group action

generalization of coordinate frame

differential geometry construct on fiber bundles

Connection on a vector bundle