Remarks on almost Riemann solitons with gradient or torse-forming vector field
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913968695541760 |
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| author | Blaga, Adara M. |
| author_facet | Blaga, Adara M. |
| contents | We consider almost Riemann solitons $(V,λ)$ in a Riemannian manifold and underline their relation to almost Ricci solitons. When $V$ is of gradient type, using Bochner formula, we explicitly express the function $λ$ by means of the gradient vector field $V$ and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_06413 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Remarks on almost Riemann solitons with gradient or torse-forming vector field Blaga, Adara M. Differential Geometry 35Q51, 53B25, 53B50 We consider almost Riemann solitons $(V,λ)$ in a Riemannian manifold and underline their relation to almost Ricci solitons. When $V$ is of gradient type, using Bochner formula, we explicitly express the function $λ$ by means of the gradient vector field $V$ and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature. |
| title | Remarks on almost Riemann solitons with gradient or torse-forming vector field |
| topic | Differential Geometry 35Q51, 53B25, 53B50 |
| url | https://arxiv.org/abs/2008.06413 |