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 $M_1{\times }_f{M}_{\perp }$ of order $1$ of a Kenmotsu manifold $\bar{M}$ 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 $\bar{M}$. The present paper deals with the study of warped product submanifolds by interchanging the two factors $M_T$ and $M_{\perp }$, i.e, the warped products of the form $M_2{\times }_f{M}_T$ such that $M_2=M_{\perp }\times M_{\theta }$. 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.

20 pages