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

Abstract

In the present paper, we discuss the non-trivial warped product pseudo slant submanifolds of type $M_{\perp }{\times }_f{M}_{\theta }$ and $M_{\theta }{\times }_f{M}_{\perp }$ 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.