In this article, we prove that compact simple Lie groups () 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, () 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.
Accepted:
Published online:
Na Xu 1; Ju Tan 1
@article{CRMATH_2019__357_7_624_0, author = {Na Xu and Ju Tan}, title = {On left-invariant {Einstein} metrics that are not geodesic orbit}, journal = {Comptes Rendus. Math\'ematique}, pages = {624--628}, publisher = {Elsevier}, volume = {357}, number = {7}, year = {2019}, doi = {10.1016/j.crma.2019.07.003}, language = {en}, }
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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