Positive Einstein Metrics with $\mathbb{S}^{4m+3}$ as Principal Orbit
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866929306699038720 |
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| author | Chi, Hanci |
| author_facet | Chi, Hanci |
| contents | We prove that there exists at least one positive Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$ for $m\geq 2$. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$. We also investigate the existence of cohomogeneity one positive Einstein metrics on $\mathbb{S}^{4m+4}$ and prove the existence of a non-standard Einstein metric on $\mathbb{S}^8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13216 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Positive Einstein Metrics with $\mathbb{S}^{4m+3}$ as Principal Orbit Chi, Hanci Differential Geometry We prove that there exists at least one positive Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$ for $m\geq 2$. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$. We also investigate the existence of cohomogeneity one positive Einstein metrics on $\mathbb{S}^{4m+4}$ and prove the existence of a non-standard Einstein metric on $\mathbb{S}^8$. |
| title | Positive Einstein Metrics with $\mathbb{S}^{4m+3}$ as Principal Orbit |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2210.13216 |