Einstein metrics on aligned homogeneous spaces with two factors
| Autor: | Lauret, Jorge, Will, Cynthia |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 23 pages, 5 figures |
| Databáze: | arXiv |
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