Complete gradient Einstein-type Sasakian manifolds with $α=0$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912831075516416 |
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| author | Maeta, Shun |
| author_facet | Maeta, Shun |
| contents | Catino, Mastrolia, Monticelli, and Rigoli have launched an ambitious program to study known geometric solitons from a unified perspective, which they term Einstein-type manifolds. This framework allows one to treat Ricci solitons, Yamabe solitons, and all of their generalizations simultaneously. Einstein-type manifolds are characterized by four constants $α, β, μ$ and $ρ$. In this paper, we show that when $α= 0$, complete gradient Einstein-type Sasakian manifolds are trivial or isometric to the unit sphere. As a consequence, many geometric solitons on Sasakian manifolds turn out to be trivial or isometric to the unit sphere. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete gradient Einstein-type Sasakian manifolds with $α=0$ Maeta, Shun Differential Geometry 53C25, 53D10, 53C21, 53C20 Catino, Mastrolia, Monticelli, and Rigoli have launched an ambitious program to study known geometric solitons from a unified perspective, which they term Einstein-type manifolds. This framework allows one to treat Ricci solitons, Yamabe solitons, and all of their generalizations simultaneously. Einstein-type manifolds are characterized by four constants $α, β, μ$ and $ρ$. In this paper, we show that when $α= 0$, complete gradient Einstein-type Sasakian manifolds are trivial or isometric to the unit sphere. As a consequence, many geometric solitons on Sasakian manifolds turn out to be trivial or isometric to the unit sphere. |
| title | Complete gradient Einstein-type Sasakian manifolds with $α=0$ |
| topic | Differential Geometry 53C25, 53D10, 53C21, 53C20 |
| url | https://arxiv.org/abs/2510.12441 |