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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, Hindawi, vol. 2025, pages 1-9, July.
    • Handle: RePEc:hin:jjmath:6067939
    DOI: 10.1155/jom/6067939
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