A study of $ * $-Ricci–Yamabe solitons on $ LP $-Kenmotsu manifolds

Abdul Haseeb; Fatemah Mofarreh; Sudhakar Kumar Chaubey; Rajendra Prasad; Abdul Haseeb; Fatemah Mofarreh; Sudhakar Kumar Chaubey; Rajendra Prasad

doi:10.3934/math.20241096

AIMS Mathematics

2024, Volume 9, Issue 8: 22532-22546. doi: 10.3934/math.20241096

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A study of $ * $-Ricci–Yamabe solitons on $ LP $-Kenmotsu manifolds

1.
Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia
2.
Mathematical Science Department, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh-11546, Kingdom of Saudi Arabia
3.
Section of Mathematics, University of Technology & Applied Sciences, Shinas, Oman
4.
Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India

Received: 11 June 2024 Revised: 10 July 2024 Accepted: 16 July 2024 Published: 22 July 2024
MSC : 53C21, 53C25, 53C50, 53C80, 53E20

In this study, we characterize $ LP $-Kenmotsu manifolds admitting $ * $-Ricci–Yamabe solitons ($ * $-RYSs) and gradient $ * $-Ricci–Yamabe solitons (gradient $ * $-RYSs). It is shown that an $ LP $-Kenmotsu manifold of dimension $ n $ admitting a $ * $-Ricci–Yamabe soliton obeys Poisson's equation. We also determine the necessary and sufficient conditions under which the Laplace equation is satisfied by $ LP $-Kenmotsu manifolds. Finally, by using a non-trivial example of an $ LP $-Kenmotsu manifold, we verify some results of our paper.
- $ * $-Ricci–Yamabe solitons,
- $ LP $-Kenmotsu manifolds,
- Einstein manifolds,
- $ \eta $-Einstein manifolds,
- Poisson's equation
Citation: Abdul Haseeb, Fatemah Mofarreh, Sudhakar Kumar Chaubey, Rajendra Prasad. A study of $ * $-Ricci–Yamabe solitons on $ LP $-Kenmotsu manifolds[J]. AIMS Mathematics, 2024, 9(8): 22532-22546. doi: 10.3934/math.20241096

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Abstract

In this study, we characterize $ LP $-Kenmotsu manifolds admitting $ * $-Ricci–Yamabe solitons ($ * $-RYSs) and gradient $ * $-Ricci–Yamabe solitons (gradient $ * $-RYSs). It is shown that an $ LP $-Kenmotsu manifold of dimension $ n $ admitting a $ * $-Ricci–Yamabe soliton obeys Poisson's equation. We also determine the necessary and sufficient conditions under which the Laplace equation is satisfied by $ LP $-Kenmotsu manifolds. Finally, by using a non-trivial example of an $ LP $-Kenmotsu manifold, we verify some results of our paper.

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