On the coincidence of group connections induced by an intrinsic composite equipment of a distribution

Abstract

In a multidimensional projective space, a distribution of planes is considered. Under the assumption that there is a relative invariant scoped by a subobject of a fundamental object of the first order, an internal composite equipment of the distribution is made, which is an analog of the Cartan equipment and Norder normalization of the second kind. It is proved that the composition equipment induces six bunches of group connections in the associated principal bundle which are intrinsically determined by the distribution itself. In every bundle, a unique intrinsic connection is distinguished. Analytic and geometric conditions for the coincidence of different types of connections are found. In the paper, the Cartan–Laptev method is used. All considerations are of local nature.