Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit
type: Item
instance of: scholarly article
title: Compact simple Lie groups admitting left-invariant Einstein metrics that are not geodesic orbit
zbMATH Open document ID: 1390.53039
author: Huibin Chen
author: Zhiqi Chen
author: Shaoqiang Deng
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2018-03-12T00:00:00Z
review text: In previous works, invariant Einstein metrics which are not naturally reductive were obtained on the compact simple Lie groups \({\mathrm{SO}}(n)\), \({\mathrm{SU}}(n)\), \({\mathrm{Sp}}(n)\), \({\mathrm{E}}_6\), \({\mathrm{E}}_7\), \({\mathrm{E}}_8\) and \({\mathrm{F}}_4\). In other works, invariant Einstein metrics which is not ``geodesic orbit'' was obtained on \({\mathrm{G}}_2\). On the present work, it is shown that the above-mentioned metrics which are not naturally reductive are neither ``geodesic orbit''. The techniques from the generalized Wallach spaces are used for the proof.
reviewed by: Zdeněk Dušek
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 6849173
zbMATH Keywords: Einstein metric
zbMATH Keywords: naturally reductive metric
zbMATH Keywords: geodesic orbit metric
MaRDI profile type: Publication
full work available at URL: j.crma.2017.11.018
OpenAlex ID: W2771589227
Wikidata QID: Q115358178
cites work: EINSTEIN METRICS ON THE SYMPLECTIC GROUP WHICH ARE NOT NATURALLY REDUCTIVE
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DOI: 10.1016/J.CRMA.2017.11.018
description: scientific article; zbMATH DE number 6849173