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http://dx.doi.org/10.5831/HMJ.2021.43.4.613

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)
Publication Information
Honam Mathematical Journal / v.43, no.4, 2021 , pp. 613-626 More about this Journal
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
Yamabe Soliton; ${\eta}$-Yamabe soliton; Lorentzian para-Kenmotsu manifolds; curvature tensor; ${\eta}$-Einstein manifold;
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