# Generalized inequalities of warped product submanifolds of nearly Kenmotsu $f$-manifolds

## TL;DR

This paper establishes sharp inequalities for the squared norm of the second fundamental form of certain warped product submanifolds in nearly Kenmotsu $f$-manifolds, extending and generalizing previous results in the field.

## Contribution

It introduces new sharp inequalities for warped product pseudo slant submanifolds in nearly Kenmotsu $f$-manifolds, including equality cases and generalizations of prior results.

## Key findings

- Derived sharp inequalities involving the second fundamental form.
- Identified conditions for equality cases.
- Extended previous results to more general warped product submanifolds.

## Abstract

In the present paper, we discuss the non-trivial warped product pseudo slant submanifolds of type $M_{\bot }\times _{f}M_{\theta }$ and $M_{\theta}\times _{f}M_{\bot }$ of nearly Kenmotsu $f$-manifold $\overline{M}$. Firstly, we get some basic properties of these type warped product submanifolds. Then, we establish the general sharp inequalities for squared norm of second fundamental form for mixed totally geodesic warped product pseudo slant submanifolds of both cases, in terms of the warping function and the slant angle. Also the equality cases are verified. We show that some previous results are trivial from our results.