Geometrization of a sheaf of first-type connections generated by a compositional frame 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 perform compositional framing of the distribution, which is an analog of the Cartan framing and the Norden normalization of the second kind. We prove that a distribution of planes and its compositional framing induce a group connection in the associated bundle. A geometric characteristic of the induced connection by parallel transfers of framing 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.