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, μ ) ' -almost Kenmotsu manifold satisfies the CPE , then the manifold is either locally isometric to the product space ℍ 2 ( − 4) × 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 the CPE conjecture, then the manifold is Einstein.