On a type of almost Kenmotsu manifolds with nullity distributions

The object of the present paper is to characterize Weyl semisymmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to the (k,μ)′-nullity distribution and (k,μ)-nullity distribution respectively. Also we characterize almost Kenmotsu manifolds satisfying the curvature condition C⋅S=0, where C and S are the Weyl conformal curvature tensor and Ricci tensor respectively with its characteristic vector field ξ belonging to the (k,μ)′-nullity distribution. As a consequence of the main results we obtain several corollaries. Finally, we present an example to verify our results.