Geometrization of a Sheaf of First-Type Connections Generated by a Compositional Equipment on a Distribution of Planes

In this paper, we continue the study of distributions of planes in the multidimensional projective space with an associated principal bundle. We construct a compositional equipment of the distribution, which is an analog of the Cartan equipment and the Norden normalization of the second kind. We prove that a distribution of planes and its compositional equipment induce a group connection in the associated bundle. A geometric characteristic of the induced connection by parallel transfers of equipping planes is given. Also, a sheaf of connections of the first type is constructed and parallel transfers in the sheaf of connections and its subconnections are described.