Another class of warped product skew CR-submanifolds of Kenmotsu manifolds

Abstract

Recently, Naghi et al. \cite{NAGHI} studied warped product skew CR-submanifold of the form $M_1\times_fM_\bot$ of order $1$ of a Kenmotsu manifold $\bar{M}$ such that $M_1=M_T\times M_\theta$, where $M_T$, $M_\bot$ and $M_\theta$ are invariant, anti-invariant and proper slant submanifolds of $\bar{M}$. The present paper deals with the study of warped product submanifolds by interchanging the two factors $M_T$ and $M_\bot$, i.e, the warped products of the form $M_2\times_fM_T$ such that $M_2=M_\bot\times M_\theta$. The existence of such warped product is ensured by an example and then we characterize such warped product submanifold. A lower bounds of the square norm of second fundamental form is derived with sharp relation, whose equality case is also considered.