Comptes Rendus
Differential geometry/Lie algebras
On left-invariant Einstein metrics that are not geodesic orbit
Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 624-628.

In this article, we prove that compact simple Lie groups SO(n) (n>12) admit at least two left-invariant Einstein metrics that are not geodesic orbit, which gives a positive answer to a problem recently posed by Nikonorov.

Dans cette Note, nous démontrons que les groupes de Lie simples, compacts, SO(n) (n>12) admettent au moins deux métriques d'Einstein invariantes à gauche, dont des géodésiques maximales ne sont pas des orbites de sous-groupes à un paramètre du groupe d'isométries complet. Ceci répond par l'affirmative à une question récemment posée par Nikonorov.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.07.003

Na Xu 1; Ju Tan 1

1 School of Mathematics and Physics, Anhui University of Technology, Maanshan, 243032, People's Republic of China
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Na Xu; Ju Tan. On left-invariant Einstein metrics that are not geodesic orbit. Comptes Rendus. Mathématique, Volume 357 (2019) no. 7, pp. 624-628. doi : 10.1016/j.crma.2019.07.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.07.003/

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