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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |