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Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi‐Type

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  • Vahid Pirhadi
  • Ghodratallah Fasihi-Ramandi
  • Shahroud Azami

Abstract

This paper is devoted to Ricci solitons admitting a Jacobi‐type vector field. First, we present some rigidity results for Ricci solitons (Mn, g, V, λ) admitting a Jacobi‐type vector field ξ and provide conditions under which ξ is Killing. We also present conditions under which the Ricci soliton (Mn, g, ξ, λ) is isometric to Rn. Then, we demonstrate that Jacobi‐type vector fields which are the potential vector fields of a quasi‐Einstein manifold are Killing and of constant length. Finally, we prove that quasi‐Einstein manifolds, where potential vector fields are Jacobi type, are necessarily of constant scalar curvature.

Suggested Citation

  • Vahid Pirhadi & Ghodratallah Fasihi-Ramandi & Shahroud Azami, 2025. "Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi‐Type," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:6067939
    DOI: 10.1155/jom/6067939
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    References listed on IDEAS

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    1. Tarak Mandal & Uday Chand De & Meraj Ali Khan & Mohammad Nazrul Islam Khan & Dengfeng Lü, 2024. "A Study on Contact Metric Manifolds Admitting a Type of Solitons," Journal of Mathematics, Hindawi, vol. 2024, pages 1-13, June.
    2. Bang-Yen Chen & Sharief Deshmukh & Amira A. Ishan, 2019. "On Jacobi-Type Vector Fields on Riemannian Manifolds," Mathematics, MDPI, vol. 7(12), pages 1-11, November.
    3. Noura Alhouiti & Soumendu Roy & Santu Dey & Fatemah Mofarreh & Akram Ali & Yanlin Li & Francisco J. Garcia-Pacheco, 2024. "Geometric Classifications of Perfect Fluid Space-Time Admit Conformal Ricci-Bourguignon Solitons," Journal of Mathematics, Hindawi, vol. 2024, pages 1-9, May.
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    Cited by:

    1. Mehdi Jafari & Amirhesam Zaeim & Adele Alemahdi, 2025. "Riemann Solitons on Homogeneous Siklos Spacetimes," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).

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