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Connection (vector bundle)

In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for which the notion of parallel transport…

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Overview

Motivation

Formal definition

Induced connections

Exterior covariant derivative and vector-valued forms

Affine properties of the set of connections

Relation to principal and Ehresmann connections

Local expression

Parallel transport and holonomy

Curvature

Gauge transformations

Examples

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Connection (vector bundle)

Nodes102
Edges101
Triples0
Avg. degree1.98
Density0.019608
Components1

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Important terminology

displaystyle connection bundle vector nabla gamma connections one section derivative parallel linear product may given operatorname mathbb space tensor exterior

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