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

TL;DR

This paper explores a new class of warped product skew CR-submanifolds in Kenmotsu manifolds by interchanging factors, providing existence conditions, characterizations, and geometric inequalities with equality cases.

Contribution

It introduces and characterizes a novel class of warped product skew CR-submanifolds by swapping factors, extending previous work on Kenmotsu manifolds.

Findings

Existence of the new warped product submanifolds is demonstrated with an example.

Characterization of these warped product submanifolds is established.

A sharp lower bound for the squared norm of the second fundamental form is derived.

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.