Sub-Riemannian quasi-statistical structures on non-holonomic Kenmotsu manifolds

Abstract

The paper is devoted to continuation of the study of almost contact metric manifolds equipped with a connection with torsion of a special type. The connection with torsion to be used is determined by the internal connection of an almost contact metric manifold and a field of endomorphisms acting on this manifold and preserving its distribution. The field of endomorphisms is called the second structural endomorphism of an almost contact metric manifold. In previous works, it has been shown that the structure of the second structural endomorphism may significantly depend on the geometry of the manifold under consideration. For example, the structure of the endomorphism, corresponding to the skew-symmetric connection, was found. In this article, we introduce and study the sub-Riemannian quasi-statistical structure on a nonholonomic Kenmotsu manifold. A non-holonomic Kenmotsu manifold possesses all properties of the Kenmotsu manifolds except for the following one: the distribution of a Kenmotsu manifold is involutive. At the core of a sub-Riemannian quasistatistical structure lies a connection with torsion of a special type. It is proved that the internal connection is consistent with the metric induced on the distribution of the manifold under consideration. The structural endomorphism corresponding to a sub-Riemannian quasi-statistical structure is described.