Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916413525983232 |
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| author | Arvanitoyeorgos, Andreas Sakane, Yusuke Statha, Marina |
| author_facet | Arvanitoyeorgos, Andreas Sakane, Yusuke Statha, Marina |
| contents | We obtain new invariant Einstein metrics on the compact Lie groups
$\SO(n)$ which are not naturally reductive. This is achieved by using the real flag manifolds $\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)$ and by imposing certain symmetry assumptions in the set of all
left-invariant metrics on $\SO(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds Arvanitoyeorgos, Andreas Sakane, Yusuke Statha, Marina Differential Geometry 53C25, 53C30, 13P10, 65H10, 68W30 We obtain new invariant Einstein metrics on the compact Lie groups $\SO(n)$ which are not naturally reductive. This is achieved by using the real flag manifolds $\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)$ and by imposing certain symmetry assumptions in the set of all left-invariant metrics on $\SO(n)$. |
| title | Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds |
| topic | Differential Geometry 53C25, 53C30, 13P10, 65H10, 68W30 |
| url | https://arxiv.org/abs/2409.18990 |