Non naturally reductive Einstein metrics on $\SU(N)$ via generalized flag manifolds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912506389200896 |
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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 group
$\SU(N)$ which are not naturally reductive.
This is achieved by using the generalized flag manifold $G/K=\SU(k_1+\cdots +k_p)/\s(\U(k_1)\times\cdots\times\U(k_p))$ and by taking an appropriate choice of orthogonal basis of the center of Lie subalgebra $\frak k$ for $K$, which poses
certain symmetry conditions to the $\Ad(K)$-invariant metrics of $\SU(N)$. We also study the isometry problem for the Einstein metrics found. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non naturally reductive Einstein metrics on $\SU(N)$ via generalized 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 group $\SU(N)$ which are not naturally reductive. This is achieved by using the generalized flag manifold $G/K=\SU(k_1+\cdots +k_p)/\s(\U(k_1)\times\cdots\times\U(k_p))$ and by taking an appropriate choice of orthogonal basis of the center of Lie subalgebra $\frak k$ for $K$, which poses certain symmetry conditions to the $\Ad(K)$-invariant metrics of $\SU(N)$. We also study the isometry problem for the Einstein metrics found. |
| title | Non naturally reductive Einstein metrics on $\SU(N)$ via generalized flag manifolds |
| topic | Differential Geometry 53C25, 53C30, 13P10, 65H10, 68W30 |
| url | https://arxiv.org/abs/2502.18491 |