On warped product gradient $η$-Ricci solitons
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866918108820668416 |
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| author | Blaga, Adara M. |
| author_facet | Blaga, Adara M. |
| contents | If the potential vector field of an $η$-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a Laplacian equation satisfied by the potential function $f$. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by $f$. We give a way to construct a gradient $η$-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_04092 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On warped product gradient $η$-Ricci solitons Blaga, Adara M. Differential Geometry 53C21, 53C44, 53C25 If the potential vector field of an $η$-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a Laplacian equation satisfied by the potential function $f$. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by $f$. We give a way to construct a gradient $η$-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature. |
| title | On warped product gradient $η$-Ricci solitons |
| topic | Differential Geometry 53C21, 53C44, 53C25 |
| url | https://arxiv.org/abs/1705.04092 |