Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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THREE-DIMENSIONAL LORENTZIAN PARA-KENMOTSU MANIFOLDS AND YAMABE SOLITONS

  • Pankaj, Pankaj (Mathematics Section, IT Department, University of Technology and Applied Sciences-Muscat) ;
  • Chaubey, Sudhakar K. (Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences-Shinas) ;
  • Prasad, Rajendra (Department of Mathematics and Astronomy, University of Lucknow)
  • Received : 2021.04.11
  • Accepted : 2021.07.12
  • Published : 2021.12.25
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Abstract

The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of three-dimensional Ricci symmetric and 𝜂-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.

Keywords

Acknowledgement

The authors express their sincere thanks to the Editor and anonymous referees for their valuable suggestions in the improvement of the paper.

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