Compact homogeneous Einstein 6-manifolds.
type: Item
instance of: scholarly article
title: Compact homogeneous Einstein 6-manifolds.
zbMATH Open document ID: 1045.53031
DOI: 10.1016/S0926-2245(03)00051-2
author: E. D. Rodionov
author: Yurii G. Nikonorov
published in: Differential Geometry and its Applications
publication date: 2004-01-04T00:00:00Z
review text: The goal of the authors is to give a classification of all compact simply connected homogeneous Einstein 6-dimensional manifolds \((M= G/H,g)\), that is to classify all invariant Einstein metrics \(g\) on 6-dimensional homogeneous simply connected spaces of a compact Lie group \(G\). Without loss of generality, one can assume that \(G\) is a compact connected semisimple Lie group. The authors prove that in this case, \((M = G/H,g )\) is either a symmetric space or one of the following manifolds : (1) \(\mathbb{C} P^3 = Sp_2/Sp_1 \times U_1\) with the sqashed metric, (2) the Wallach space \(SU_3/T^2\) with the standard metric or with the Kähler invariant metric, (3) the Lie group \(SU_2 \times SU_2\) with some left invariant Einstein metric. This reduces the problem to the classification of left invariant Einstein metrics on the group \(G= SU_2 \times SU_2\). The authors get the following partial result in this direction: If the Einstein metric \(g\) is right invariant with respect to a subgroup \(T^1\) of \(G\), then it is homothetic to the standard biinvariant metric or to the Jensen metric.
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 2021018
zbMATH Keywords: Homogeneous Einstein manifolds
zbMATH Keywords: invariant Einstein metrics
zbMATH Keywords: homogeneous manifolds
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
Wikidata QID: Q115337998
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full work available at URL: s0926-2245(03)00051-2
OpenAlex ID: W1999171251
description: scientific article; zbMATH DE number 2021018