Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit

Huibin Chen; Zhiqi Chen; Shaoqiang Deng

doi:10.1016/j.crma.2017.11.018

Geometry

Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit

Presented by: Claire Voisin

Huibin Chen ¹; Zhiqi Chen ¹; Shaoqiang Deng ¹

¹ School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China

Comptes Rendus. Mathématique, Volume 356 (2018) no. 1, pp. 81-84.

Abstract
Résumé

In this article, we prove that the compact simple Lie groups $S U (n)$ for $n \geq 6$ , $S O (n)$ for $n \geq 7$ , $S p (n)$ for $n \geq 3$ , $E_{6}, E_{7}, E_{8}$ , and $F_{4}$ 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 $S U (n)$ pour $n \geq 6$ , $S O (n)$ pour $n \geq 7$ , $S p (n)$ pour $n \geq 3$ , $E_{6}$ , $E_{7}$ , $E_{8}$ et $F_{4}$ 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.

Received: 2017-10-18
Accepted: 2017-11-30
Published online: 2017-12-06

DOI: 10.1016/j.crma.2017.11.018

Author's affiliations:

Huibin Chen ¹; Zhiqi Chen ¹; Shaoqiang Deng ¹

¹ School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China

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     author = {Huibin Chen and Zhiqi Chen and Shaoqiang Deng},
     title = {Compact simple {Lie} groups admitting left-invariant {Einstein} metrics that are not geodesic orbit},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {81--84},
     publisher = {Elsevier},
     volume = {356},
     number = {1},
     year = {2018},
     doi = {10.1016/j.crma.2017.11.018},
     language = {en},
}

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Huibin Chen; Zhiqi Chen; Shaoqiang Deng. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.11.018/

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

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