Almost $η$-Ricci and almost $η$-Yamabe solitons with torse-forming potential vector field
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866916873878110208 |
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| author | Blaga, Adara M. Özgür, Cihan |
| author_facet | Blaga, Adara M. Özgür, Cihan |
| contents | We provide properties of almost $η$-Ricci and almost $η$-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold $\left(\widetilde{M},\widetilde{g} \right)$ whose potential vector field is the tangential component of a torse-forming vector field on $\widetilde{M}$, treating also the case of a minimal or pseudo quasi-umbilical hypersurface. Moreover, we give necessary and sufficient conditions for an orientable hypersurface of the unit sphere to be an almost $η$-Ricci or an almost $η$-Yamabe soliton in terms of the second fundamental tensor field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_12574 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Almost $η$-Ricci and almost $η$-Yamabe solitons with torse-forming potential vector field Blaga, Adara M. Özgür, Cihan Differential Geometry We provide properties of almost $η$-Ricci and almost $η$-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold $\left(\widetilde{M},\widetilde{g} \right)$ whose potential vector field is the tangential component of a torse-forming vector field on $\widetilde{M}$, treating also the case of a minimal or pseudo quasi-umbilical hypersurface. Moreover, we give necessary and sufficient conditions for an orientable hypersurface of the unit sphere to be an almost $η$-Ricci or an almost $η$-Yamabe soliton in terms of the second fundamental tensor field. |
| title | Almost $η$-Ricci and almost $η$-Yamabe solitons with torse-forming potential vector field |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2003.12574 |