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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09833 |
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| _version_ | 1866909390895841280 |
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| author | Guzman, Mikhail R. |
| author_facet | Guzman, Mikhail R. |
| contents | Let $ M = G/K $ be a full flag manifold. In this work, we investigate the $ G$-stability of Einstein metrics on $M$ and analyze their stability types, including coindices, for several cases. We specifically focus on $F(n) = \mathrm{SU}(n)/T$, emphasizing $n = 5$, where we identify four new Einstein metrics in addition to known ones. Stability data, including coindex and Hessian spectrum, confirms that these metrics on $F(5)$ are pairwise non-homothetic, providing new insights into the finiteness conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Einstein metrics on the full flag $F(n)$ Guzman, Mikhail R. Differential Geometry Let $ M = G/K $ be a full flag manifold. In this work, we investigate the $ G$-stability of Einstein metrics on $M$ and analyze their stability types, including coindices, for several cases. We specifically focus on $F(n) = \mathrm{SU}(n)/T$, emphasizing $n = 5$, where we identify four new Einstein metrics in addition to known ones. Stability data, including coindex and Hessian spectrum, confirms that these metrics on $F(5)$ are pairwise non-homothetic, providing new insights into the finiteness conjecture. |
| title | Einstein metrics on the full flag $F(n)$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.09833 |