Critical point equation on almost Kenmotsu manifolds - De, U. C.; Mandal, K. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
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 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.