New homogeneous Einstein metrics on \(\mathrm{SO}(7)/T\)
type: Item
instance of: scholarly article
title: New homogeneous Einstein metrics on \(\mathrm{SO}(7)/T\)
zbMATH Open document ID: 1385.53039
author: Yu Wang
author: Tianzeng Li
author: Guosong Zhao
published in: Chinese Annals of Mathematics. Series B
publication date: 2018-02-14T00:00:00Z
review text: Generalized flag manifolds are homogeneous manifolds \(M=G/C(T)\), where \(C(T)\) is the centralizer of a torus \(T\) in \(G\). In the case \(C(T)=T\), we have the full flag manifold \(M=G/T\). In simple cases of full flag manifolds, invariant Einstein metrics on them were described in previous works. In the present paper, invariant Einstein metrics on the full flag manifold \(M=\mathrm{SO}(7)/T\) are studied. This manifold has nine isotropy summands and the Einstein equations are rather complicated. The 48 solutions are determined numerically and it is shown that only 5 of them are mutually non-isometric. One Einstein metric is Kähler and four of them are non-Kähler.
reviewed by: Zdeněk Dušek
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 17B22
zbMATH DE Number: 6838916
zbMATH Keywords: generalized flag manifold
zbMATH Keywords: full flag manifold
zbMATH Keywords: Einstein metric
MaRDI profile type: Publication
full work available at URL: s11401-018-1054-8
OpenAlex ID: W2781563942
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DOI: 10.1007/S11401-018-1054-8
description: scientific article; zbMATH DE number 6838916