On some $3$-dimensional almost $η$-Ricci solitons with diagonal metrics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918108889874432 |
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| author | Blaga, Adara M. |
| author_facet | Blaga, Adara M. |
| contents | We study some properties of a $3$-dimensional manifold with a diagonal Riemannian metric as an almost $η$-Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if $η$ is given; we get constraints on the metric when the potential vector field has a particular expression; we compute the defining functions of the soliton when both the potential vector field and the $1$-form are prescribed. Moreover, we find conditions for the manifold to be flat. Based on the theoretical results, we provide examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some $3$-dimensional almost $η$-Ricci solitons with diagonal metrics Blaga, Adara M. Differential Geometry We study some properties of a $3$-dimensional manifold with a diagonal Riemannian metric as an almost $η$-Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if $η$ is given; we get constraints on the metric when the potential vector field has a particular expression; we compute the defining functions of the soliton when both the potential vector field and the $1$-form are prescribed. Moreover, we find conditions for the manifold to be flat. Based on the theoretical results, we provide examples. |
| title | On some $3$-dimensional almost $η$-Ricci solitons with diagonal metrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2406.12533 |