"In mathematics, 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. If the fiber bundle is a vector bundle, then the notion of parallel transport must be linear. Such a connection is equivalently specified by a covariant derivative, which is an operator that can differentiate sections of that bundle along tangent directions in the base manifold."@en .