Critical Point Equation on Almost Kenmotsu Manifolds

We study the critical point equation (CPE) conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional (k, mu)'-almost Kenmotsu manifold satisfies theCPE, then the manifold is either locally isometric to the product space & x210d;(2)(-4) x Double-struck capital R or the manifold is a Kenmotsu manifold. Further, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies theCPEconjecture, then the manifold is Einstein.