Einstein metrics on aligned homogeneous spaces with two factors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915159747854336 |
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| author | Lauret, Jorge Will, Cynthia |
| author_facet | Lauret, Jorge Will, Cynthia |
| contents | Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and non-existence pieces of C. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Einstein metrics on aligned homogeneous spaces with two factors Lauret, Jorge Will, Cynthia Differential Geometry Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and non-existence pieces of C. |
| title | Einstein metrics on aligned homogeneous spaces with two factors |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.00456 |