Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type
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...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/6067939 |
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| author | Vahid Pirhadi Ghodratallah Fasihi-Ramandi Shahroud Azami |
| author_facet | Vahid Pirhadi Ghodratallah Fasihi-Ramandi Shahroud Azami |
| author_sort | Vahid Pirhadi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-414800a8f19242ff9c4ff84c28b4adff |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-414800a8f19242ff9c4ff84c28b4adff2025-08-20T03:49:55ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/6067939Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-TypeVahid Pirhadi0Ghodratallah Fasihi-Ramandi1Shahroud Azami2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThis 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.http://dx.doi.org/10.1155/jom/6067939 |
| spellingShingle | Vahid Pirhadi Ghodratallah Fasihi-Ramandi Shahroud Azami Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type Journal of Mathematics |
| title | Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type |
| title_full | Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type |
| title_fullStr | Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type |
| title_full_unstemmed | Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type |
| title_short | Ricci Solitons and Generalized Ricci Solitons Whose Potential Vector Fields Are Jacobi-Type |
| title_sort | ricci solitons and generalized ricci solitons whose potential vector fields are jacobi type |
| url | http://dx.doi.org/10.1155/jom/6067939 |
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