Geometry
Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit
Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 81-84.

In this article, we prove that the compact simple Lie groups SU(n) for n6, SO(n) for n7, Sp(n) for n3, 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 n6, SO(n) pour n7, Sp(n) pour n3, 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.

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Accepted:
Published online:
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, Volume 356 (2018) no. 1, pp. 81-84. doi : 10.1016/j.crma.2017.11.018. http://www.numdam.org/articles/10.1016/j.crma.2017.11.018/

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Supported by NSFC (No. 11671212, 51535008) of China.