$$*$$-Critical point equation on a class of almost Kenmotsu manifolds

Abstract

In the present paper, we characterize $$(k,\mu )'$$-almost Kenmotsu manifolds admitting $$*$$-critical point equation. It is shown that if $$(g, \lambda )$$ is a non-constant solution of the $$*$$-critical point equation of a connected non-compact $$(k,\mu )'$$-almost Kenmotsu manifold, then (1) the manifold M is locally isometric to $$\mathbb {H}^{n+1}(-4)$$$$\times $$$$\mathbb {R}^n$$, (2) the manifold M is $$*$$-Ricci flat and (3) the function $$\lambda $$ is harmonic. Finally an illustrative example is presented.