The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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GENERALIZED RICCI SOLITONS ON 3-DIMENSIONAL CONTACT METRIC MANIFOLDS

  • Pradip Majhi (Department of Pure Mathematics, University of Calcutta) ;
  • Raju Das (Department of Pure Mathematics, University of Calcutta)
  • Received : 2023.10.16
  • Accepted : 2024.07.24
  • Published : 2024.11.30
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Abstract

In the present paper we study 3-dimensional contact metric manifolds with 𝜑Q = Q𝜑 admitting generalized Ricci solitons and generalized gradient Ricci solitons. It is proven that if a 3-dimensional contact metric manifold satisfying 𝜑Q = Q𝜑 admits a generalized Ricci soliton with non zero soliton vector field V being pointwise collinear with the characteristic vector field ξ, then the manifold is Sasakian. Also it is shown that if a 3-dimensional compact contact metric manifold with 𝜑Q = Q𝜑 admits a generalized gradient Ricci soliton then either the soliton is trivial or the manifold is flat or the scalar curvature is constant.

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Acknowledgement

The second author is financially supported by the council of scientific and industrial research, India (File no. 09/0028(11991)/2021-EMR-I). The authors are thankful to the Referee for his/her constructive suggestions in improving the paper.

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