Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type - Vahid Pirhadi; Ghodratallah Fasihi-Ramandi; Shahroud Azami (Journal of Mathematics)
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.