Abstract
In this paper, we give a local characterization for the Ricci tensor of an almost Kenmotsu [Formula: see text]-manifold [Formula: see text] to be cyclic-parallel. As an application, we prove that if [Formula: see text] has cyclic-parallel Ricci tensor and satisfies [Formula: see text], (where [Formula: see text] is the Lie derivative of [Formula: see text] along the Reeb flow and both [Formula: see text] and [Formula: see text] are smooth functions such that [Formula: see text] is invariant along the contact distribution), then [Formula: see text] is locally isometric to either the hyperbolic space [Formula: see text] or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.
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