On a Classifcation of Almost Kenmotsu Manifolds with Generalized ( ĸ, µ )′-nullity Distribution
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In the present paper we prove that in an almost Kenmotsu manifold with generalized ( ĸ, µ )- nullity distribution the three conditions:(i) the Ricci tensor of M^{2n+1} is of Codazzi type,(ii) the manifold M^{2n+1} satisfies div C=0,(iii) the manifold M^{2n+1} is locally isometric to H^{n+1}(-4)\times\mathbb{R}^{n},are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to H^{n+1}(-4)\times\mathbb{R}^{n}.
Abstract
In the present paper we prove that in an almost Kenmotsu manifold with generalized ( ĸ, µ )- nullity distribution the three conditions:(i) the Ricci tensor of M^{2n+1} is of Codazzi type,(ii) the manifold M^{2n+1} satisfies div C=0,(iii) the manifold M^{2n+1} is locally isometric to H^{n+1}(-4)\times\mathbb{R}^{n},are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to H^{n+1}(-4)\times\mathbb{R}^{n}.
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