Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Generalized Quasi-Einstein Metrics and Contact Geometry

  • Biswas, Gour Gopal (Department of Mathematics, University of Kalyani) ;
  • De, Uday Chand (Department of Pure Mathematics, University of Calcutta) ;
  • Yildiz, Ahmet (Education Faculty, Department of Mathematics, Inonu University)
  • Received : 2021.02.15
  • Accepted : 2022.02.10
  • Published : 2022.09.30
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Abstract

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

Keywords

Acknowledgement

The authors would like to thank the referees and editor for reviewing the paper carefully and their valuable comments to improve the quality of the paper.

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