Geodesic
Geometry
Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit
[Groupes de Lie simples compacts admettant des métriques d'Einstein invariantes à gauche, dont une géodésique n'est pas une orbite]

Présenté par : Claire Voisin

Chen, Huibin1 ; Chen, Zhiqi1 ; Deng, Shaoqiang1
1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Tome 356 (2018) no. 1, pp. 81-84.

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In this article, we prove that the compact simple Lie groups SU(n) for n≥6, SO(n) for n≥7, Sp(n) for n≥3, E6,E7,E8, and F4 admit left-invariant Einstein metrics that are not geodesic orbit. This gives a positive answer to an open problem recently posed by Nikonorov.

Dans cet article, nous démontrons que les groupes simples compacts SU(n) pour n≥6, SO(n) pour n≥7, Sp(n) pour n≥3, E6, E7, E8 et F4 admettent des métriques d'Einstein invariantes à gauche, dont une géodésique maximale n'est pas une orbite d'un sous-groupe à un paramètre du groupe des isométries complet. Ceci fournit une réponse positive à un problème récemment posé par Nikonorov.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.11.018

Chen, Huibin 1 ; Chen, Zhiqi 1 ; Deng, Shaoqiang 1

1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China 
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Chen, Huibin; Chen, Zhiqi; Deng, Shaoqiang. Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit. Comptes Rendus. Mathématique, Tome 356 (2018) no. 1, pp. 81-84. doi : 10.1016/j.crma.2017.11.018. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2017.11.018/

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