On almost Kenmotsu manifolds with generalized nullity distribution

Abstract

The object of the present paper is to classify generalized $(k,\mu)'$- almost Kenmotsu manifolds satisfying certain semisymmetry conditions. We prove that Weyl semisymmetric and $h'$-semisymmetric almost Kenmotsu manifolds with generalized $(k,\mu)'$- nullity distribution are both locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4)\times \mathbb{R}^{n}$. Also we characterize Weyl Ricci semisymmetric almost Kenmotsu manifolds with generalized $(k,\mu)'$-nullity distribution.