On Semi-Invariant Submanifoldsof A Nearly Hyperbolic Kenmotsu Manifold With Semi-Symmetric Semi-Metric Connection

Abstract

Weconsiders a nearly hyperbolic Kenmotsu manifold admitting a semi-symmetric semi-metric connection and study semi-invariant submanifolds of a nearly hyperbolic Kenmotsu manifold with semisymmetric semi-metric connection. We also find the integrability conditions of some distributions on nearly hyperbolic Kenmotsu manifold and study parallel distributions (horizontal & vertical distributions) on nearly hyperbolic Kenmotsu manifold.

On Semi-Invariant Submanifolds of Trans-Sasakian Finsler Manifolds

“…Besides, Kobayashi studied semi-invariant submanifolds for a certain class of almost contact manifolds in [3] in 1986. Afterwards, semi invariant submanifolds of several structures are discussed like nearly trans-Sasakian and nearly Kenmotsu manifolds in [4], in 2004 and in [5], in 2009. Also, Shahid got some fundamental results on almost semi-invariant submanifolds of trans-Sasakian manifolds in [6], in 1993.…”

Semi-invariant submanifolds of a Kenmotsu manifold with a generalized almost r-contact structure admitting a semi-symmetric metric connection

“…On the other hand, A. Bejancu, introduced the notion of semi-invariant submanifolds [6] or contact CR-submanifolds [5], as a generalization of invariant and anti-invariant submanifolds of an almost contact metric manifold and was followed by several geometers in [1,2,4,7,11,12]. Semi-invariant submanifolds of a Kenmotsu manifold immersed in a generalized almost r-contact metric structure was defined and studied by R. Nivas and S. Yadav [13].…”