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AIMS Mathematics

2026, Volume 11, Issue 6: 15831-15850. doi: 10.3934/math.2026652
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$ LP $-Kenmotsu manifolds admitting almost $ * $-Ricci-Bourguignon solitons and gradient almost $ * $-Ricci-Bourguignon solitons

  • 1.
    Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia
  • 2.
    Unit of Sciences and Mathematics, Department of Supportive Requirements, University of Technology and Applied Sciences, Shinas, P.O. Box 77, Postal Code 324, Al Aqar, Oman
  • 3.
    Mathematical Science Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia
  • Published: 04 June 2026

  • MSC : 53C21, 53C25, 53C80, 53D10, 53E20

  • In this work, a solitonic study of $ LP $-Kenmotsu $ n $-manifolds (in brief $ (LPK)_n $) was performed. Key properties of almost $ * $-RBSs are established, thus generalizing some of the known results. Additionally, we examine gradient almost $ * $-RBSs, thereby deriving conditions for the realization of the soliton structure. These results provide new insights into the theory of Ricci-Bourguignon solitons and geometric flows in semi-Riemannian manifolds. It is proven that an $ (LPK)_n $ that admits an almost $ * $-RBSs or a gradient almost $ * $-RBSs is a generalized $ \omega $-Einstein spacetime. Moreover, under certain assumptions, an $ (LPK)_n $ that admits an almost $ * $-RBSs or a gradient almost $ * $-RBSs is a perfect fluid spacetime.

    Citation: Abdul Haseeb, Sudhakar Kumar Chaubey, Fatemah Mofarreh. $ LP $-Kenmotsu manifolds admitting almost $ * $-Ricci-Bourguignon solitons and gradient almost $ * $-Ricci-Bourguignon solitons[J]. AIMS Mathematics, 2026, 11(6): 15831-15850. doi: 10.3934/math.2026652

    Related Papers:

  • In this work, a solitonic study of $ LP $-Kenmotsu $ n $-manifolds (in brief $ (LPK)_n $) was performed. Key properties of almost $ * $-RBSs are established, thus generalizing some of the known results. Additionally, we examine gradient almost $ * $-RBSs, thereby deriving conditions for the realization of the soliton structure. These results provide new insights into the theory of Ricci-Bourguignon solitons and geometric flows in semi-Riemannian manifolds. It is proven that an $ (LPK)_n $ that admits an almost $ * $-RBSs or a gradient almost $ * $-RBSs is a generalized $ \omega $-Einstein spacetime. Moreover, under certain assumptions, an $ (LPK)_n $ that admits an almost $ * $-RBSs or a gradient almost $ * $-RBSs is a perfect fluid spacetime.



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