The critical point equation on Kenmotsu and almost Kenmotsu manifolds

In this paper, we study the critical point equation (shortly, CPE) within the framework of Kenmotsu and almost Kenmotsu manifolds. First, we prove that a complete Kenmotsu metric satisfying the CPE is Einstein and locally isometric to the hyperbolic space $\mathbb{H}^{2n+1}$. In the case of Kenmotsu manifolds, it is possible to determine the potential function explicitly (locally). We also provide some examples of Kenmotsu and almost Kenmotsu manifolds that satisfy the CPE.