Ricci curvature and Einstein metrics on aligned homogeneous spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914975871664128 |
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| author | Lauret, Jorge Will, Cynthia |
| author_facet | Lauret, Jorge Will, Cynthia |
| contents | Let $M=G/K$ be a compact homogeneous space and assume that $G$ and $K$ have many simple factors. We show that the topological condition of having maximal third Betti number, in the sense that $b_3(M)=s-1$ if $G$ has $s$ simple factors, so called {\it aligned}, leads to a relatively manageable algebraic structure on the isotropy representation, paving the way to the computation of Ricci curvature formulas for a large class of $G$-invariant metrics. As an application, we study the existence and classification of Einstein metrics on aligned homogeneous spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ricci curvature and Einstein metrics on aligned homogeneous spaces Lauret, Jorge Will, Cynthia Differential Geometry Let $M=G/K$ be a compact homogeneous space and assume that $G$ and $K$ have many simple factors. We show that the topological condition of having maximal third Betti number, in the sense that $b_3(M)=s-1$ if $G$ has $s$ simple factors, so called {\it aligned}, leads to a relatively manageable algebraic structure on the isotropy representation, paving the way to the computation of Ricci curvature formulas for a large class of $G$-invariant metrics. As an application, we study the existence and classification of Einstein metrics on aligned homogeneous spaces. |
| title | Ricci curvature and Einstein metrics on aligned homogeneous spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.13058 |