The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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SASAKIAN 3-MANIFOLDS SATISFYING SOME CURVATURE CONDITIONS ASSOCIATED TO Ƶ-TENSOR

  • Dey, Dibakar (Department of Pure Mathematics, University of Calcutta) ;
  • Majhi, Pradip (Department of Pure Mathematics, University of Calcutta)
  • Received : 2021.03.16
  • Accepted : 2021.04.15
  • Published : 2021.05.31
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Abstract

In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

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Acknowledgement

The authors would like to thank the anonymous referee for his/her valuable comments.

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