A general inequality for pointwise semi-slant warped products in nearly Kenmotsu manifolds

Abstract

In this paper, we prove that every pointwise semi-slant warped product submanifold $M=N^T\times_fN^\theta$ in a nearly Kenmotsu manifold $\tilde M$ satisfies the following inequality: $\|h\|^2\geq 2n_2\left(1+\frac{10}{9}\cot^2\theta\right)\left(\|\hat\nabla(\ln f)\|^2-1\right),$ where $n_2=\dim N^\theta,\;\hat\nabla(\ln f)$ is the gradient of $\ln f$ and $\|h\|$ is the length of the second fundamental form of $M$. The equality and special cases of the inequality iare investigated.