Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911494194593792 |
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| author | Chi, Hanci |
| author_facet | Chi, Hanci |
| contents | We establish the existence of two 3-parameter families of non-Einstein, non-shrinking Ricci solitons: one on $\mathbb{H}^{m+1}$ and one on $\mathbb{HP}^{m+1}\backslash\{*\}$. Each family includes a continuous 1-parameter subfamily of asymptotically paraboloidal (non-collapsed) steady Ricci solitons, with the Jensen sphere as the base. Additionally, we extend this result by proving the existence of a 2-parameter family on $\mathbb{O}^2$, which contains a 1-parameter subfamily of asymptotically paraboloidal steady Ricci solitons based on the Bourguignon--Karcher sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration Chi, Hanci Differential Geometry 53E20 (primary), 53C25 (secondary) We establish the existence of two 3-parameter families of non-Einstein, non-shrinking Ricci solitons: one on $\mathbb{H}^{m+1}$ and one on $\mathbb{HP}^{m+1}\backslash\{*\}$. Each family includes a continuous 1-parameter subfamily of asymptotically paraboloidal (non-collapsed) steady Ricci solitons, with the Jensen sphere as the base. Additionally, we extend this result by proving the existence of a 2-parameter family on $\mathbb{O}^2$, which contains a 1-parameter subfamily of asymptotically paraboloidal steady Ricci solitons based on the Bourguignon--Karcher sphere. |
| title | Non-Shrinking Ricci Solitons of cohomogeneity one from the quaternionic Hopf fibration |
| topic | Differential Geometry 53E20 (primary), 53C25 (secondary) |
| url | https://arxiv.org/abs/2411.00581 |