*-Ricci tensor on almost Kenmotsu 3-manifolds

In this paper, we obtain the expressions of the *-Ricci operator of a three-dimensional almost Kenmotsu manifold M-3 and find that the *-Ricci tensor is not symmetric for M-3. We obtain a necessary and sufficient condition for the *-Ricci tensor to be symmetric and proved that if the *-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-h-manifold M-3 is symmetric, then M-3 is locally isometric to a three-dimensional non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. Further, it is shown that the *-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-manifold M-3 is parallel if and only if M-3 is *-Ricci flat. In addition, M-3 satisfying del(xi)h = 0 is locally isometric to H-2(-4) x R. Finally, we discuss about eta-parallel *-Ricci tensor on almost Kenmotsu 3-manifolds.