In the present paper we prove that in an almost Kenmotsu manifold with generalized (k, μ)′-nullity distribution the three conditions: (i) the Ricci tensor of M²ⁿ⁺¹ is of Codazzi type, (ii) the manifold M²ⁿ⁺¹ satisfies div C = 0, (iii) the manifold M²ⁿ⁺¹ is locally isometric to Hⁿ⁺¹(−4) × ℝⁿ, are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to Hⁿ⁺¹(−4) × ℝⁿ.

Keywords: almost Kenmotsu manifold, generalized nullity distribution, Codazzi type of Ricci tensor, cyclic parallel Ricci tensor, div C = 0