ζ -Conformally Flat LP -Kenmotsu Manifolds and Ricci–Yamabe Solitons

Abdul Haseeb (), Mohd Bilal, Sudhakar K. Chaubey and Abdullah Ali H. Ahmadini
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Abdul Haseeb: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
Mohd Bilal: Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al Qura University, Makkah 21955, Saudi Arabia
Sudhakar K. Chaubey: Section of Mathematics, Department of IT, University of Technology and Applied Sciences, Shinas 324, Oman
Abdullah Ali H. Ahmadini: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia

Mathematics, 2022, vol. 11, issue 1, 1-14

Abstract: In the present paper, we characterize m -dimensional ζ -conformally flat L P -Kenmotsu manifolds (briefly, ( L P K ) m ) equipped with the Ricci–Yamabe solitons (RYS) and gradient Ricci–Yamabe solitons (GRYS). It is proven that the scalar curvature r of an ( L P K ) m admitting an RYS satisfies the Poisson equation Δ r = 4 ( m − 1 ) δ { β ( m − 1 ) + ρ } + 2 ( m − 3 ) r − 4 m ( m − 1 ) ( m − 2 ) , where ρ , δ ( ≠ 0 ) ∈ R . In this sequel, the condition for which the scalar curvature of an ( L P K ) m admitting an RYS holds the Laplace equation is established. We also give an affirmative answer for the existence of a GRYS on an ( L P K ) m . Finally, a non-trivial example of an L P -Kenmotsu manifold ( L P K ) of dimension four is constructed to verify some of our results.

Keywords: Lorentzian manifolds; Ricci–Yamabe solitons; gradient Ricci–Yamabe solitons; perfect fluid spacetime; Einstein manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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