no. 7
Differential geometry/Lie algebras
On left-invariant Einstein metrics that are not geodesic orbit
[Sur les métriques d'Einstein invariantes à gauche, qui ne sont pas à orbites géodésiques]

Présenté par : the Editorial Board

Xu, Na1 ; Tan, Ju1
1 School of Mathematics and Physics, Anhui University of Technology, Maanshan, 243032, People's Republic of China
Comptes Rendus. Mathématique, Tome 357 (2019) no. 7, pp. 624-628.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.07.003
Xu, Na 1 ; Tan, Ju 1

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

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