$CR$-Submanifolds of a Nearly Trans-Hyperbolic Sasakian Manifold with a Semi-Symmetric Non-Metric Connection

Abstract

In this paper, $CR$-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection are studied. The parallel distributions relating to $\xi$-vertical and $\xi$-horizontal $CR$-submanifolds of nearly trans-hyperbolic Sasakian manifold with a semi symmetric non-metric connection are obtained. Moreover, Nijenhuis tensor is calculated and integrability conditions of the distributions on $CR$ submanifolds of nearly trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection are discussed.