Distributions in CR-lightlike submanifolds of an indefinite Kaehler statistical manifold

Abstract

In this paper, the distributions in CR-lightlike submanifolds of an indefinite Kaehler Statistical manifold have been characterized using second fundamental form and the necessary and sufficient conditions for integrability of the same have been obtained. Also, the conditions for the distributions to be totally geodesic with respect to the dual connections in the statistical manifold have been developed.

STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection

“…Statistical manifolds, which analyze the geometric structures on sets of certain probability distributions were initiated by [20] and thereafter developed by various researchers [1], [2], [12] and [17] et al In this context, the lightlike theory of statistical manifolds has been investigated by [3], [4], and many others. Further, by consolidating the notion of statistical manifold with an indefinite Kaehler manifold, several findings have been demonstrated for the CR-lightlike submanifolds and hypersurfaces of an indefinite Kaehler statistical manifold by [15], [18], [19]. [13] introduced a quarter symmetric linear connection as: A linear connection ∇ on a Riemannian manifold ( M , g) is said to be a quarter symmetric connection if its torsion tensor T satisfies…”