Skew connections in vector bundles and their prolongations

Abstract

The paper is closely related to [1] and [2]. A skew connection in a vector bundleEas defined here is a pseudo-connection (in the sense of [1]) which can be changed into a connection by transforming separately the bundleEitself and the bundle of its differentials, i.e. one-forms on the base with values inE. The properties of skew connections are thus expected to be only “algebraically” more complicated than those of connections; especially one can follow the pattern of [1], and prolong them to obtain higher order semi-holonomic and non-holonomic pseudo-connections. It is shown in this paper that under some circumstances the main theorem of [1] or [2] applies also to skew connections.