On a Classification of Almost Kenmotsu Manifolds with Generalized (κ,μ)'-nullity Distribution.

In the present paper we prove that in an almost Kenmotsu manifold with generalized (κ,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) x 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) x Rn. [ABSTRACT FROM AUTHOR]