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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Abdul Haseeb & Mohd Bilal & Sudhakar K. Chaubey & Abdullah Ali H. Ahmadini, 2022. "ζ -Conformally Flat LP -Kenmotsu Manifolds and Ricci–Yamabe Solitons," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:212-:d:1021447
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    References listed on IDEAS

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    1. Abdul Haseeb & Rajendra Prasad & Fatemah Mofarreh & Meraj Ali Khan, 2022. "Sasakian Manifolds Admitting ∗-η-Ricci-Yamabe Solitons," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-7, May.
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