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http://dx.doi.org/10.5666/KMJ.2018.58.1.137

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

Ghosh, Gopal (Department of Pure Mathematics, University of Calcutta)
Majhi, Pradip (Department of Pure Mathematics, University of Calcutta)
Chand De, Uday (Department of Pure Mathematics, University of Calcutta)
Publication Information
Kyungpook Mathematical Journal / v.58, no.1, 2018 , pp. 137-148 More about this Journal
Abstract
In the present paper we prove that in an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}-nullity$ 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 $H^{n+1}(-4){\times}R^n$, are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to $H^{n+1}(-4){\times}\mathbb{R}^n$.
Keywords
almost Kenmotsu manifold; generalized nullity distribution; Codazzi type of Ricci tensor; cyclic parallel Ricci tensor; div C = 0;
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Times Cited By KSCI : 1  (Citation Analysis)
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