New Einstein metrics on the Lie group $SO(n)$ which are not naturally reductive
| Autor: | Arvanitoyeorgos, Andreas, Sakane, Yusuke, Statha, Marina |
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| Rok vydání: | 2015 |
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| Zdroj: | Geom. Imaging Comput. 2 (2) (2015) |
| Druh dokumentu: | Working Paper |
| Popis: | We obtain new invariant Einstein metrics on the compact Lie groups $SO(n)$ ($n \geq 7$) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on $SO(n)$ and by computing the Ricci tensor for such metrics. The Einstein metrics are obtained as solutions of systems polynomial equations, which we manipulate by symbolic computations using Gr\"obner bases. Comment: 25 pages. arXiv admin note: text overlap with arXiv:1311.1579 |
| Databáze: | arXiv |
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