Almost Kenmotsu manifolds with constant Reeb or $\phi$-sectional curvatures

Abstract

In this paper, we prove that an almost Kenmotsu manifold M has constant Reeb sectional curvatures if and only if M has conformal Reeb foliation. On an almost Kenmotsu h-a-manifold of dimension three having constant \phi-sectional curvature, the Reeb vector field is an eigenvector field of the Ricci operator if and only if the manifold is locally isometric to a non-unimodular Lie group.