Kyungpook Mathematical Journal

  • 제58권1호
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  • Pages.137-148
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  • 2018
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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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)
  • 투고 : 2017.05.03
  • 심사 : 2018.03.14
  • 발행 : 2018.03.23
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초록

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 $H^{n+1}(-4){\times}\mathbb{R}^n$.

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참고문헌

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