Warped product skew CR-submanifolds of Kenmotsu manifolds and their applications

Abstract

In this paper, we introduce the notion of warped product skew CR-submanifolds in Kenmotsu manifolds. We obtain several results on such submanifolds. A characterization for skew CR-submanifolds is obtained. Furthermore, we establish an inequality for the squared norm of the second fundamental form of a warped product skew CR-submanifold $M_1\times_fM_{\perp}$ of order $1$ in a Kenmotsu manifold $\tilde M$ in terms of the warping function such that $M_1=M_T\times M_\theta$, where $M_T$,~ $M_\perp$ and $M_\theta$ are invariant, anti-invariant and proper slant submanifolds of $\tilde M$, respectively. Finally, some applications of our results are given.