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

Vahid Pirhadi, Ghodratallah Fasihi-Ramandi and Shahroud Azami

Journal of Mathematics, 2025, vol. 2025, 1-9

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.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2025/6067939.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2025/6067939.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6067939

DOI: 10.1155/jom/6067939

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().