{"title":"Homogeneous Einstein metrics and butterflies","authors":"Christoph Böhm, Megan M. Kerr","doi":"10.1007/s10455-023-09905-0","DOIUrl":null,"url":null,"abstract":"<div><p>In 2012, M. M. Graev associated to a compact homogeneous space <i>G</i>/<i>H</i> a nerve <span>\\({\\text {X}}_{G/H}\\)</span>, whose non-contractibility implies the existence of a <i>G</i>-invariant Einstein metric on <i>G</i>/<i>H</i>. The nerve <span>\\({\\text {X}}_{G/H}\\)</span> is a compact, semi-algebraic set, defined purely Lie theoretically by intermediate subgroups. In this paper we present a detailed description of the work of Graev and the curvature estimates given by Böhm in 2004.\n</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Global Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-023-09905-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
In 2012, M. M. Graev associated to a compact homogeneous space G/H a nerve \({\text {X}}_{G/H}\), whose non-contractibility implies the existence of a G-invariant Einstein metric on G/H. The nerve \({\text {X}}_{G/H}\) is a compact, semi-algebraic set, defined purely Lie theoretically by intermediate subgroups. In this paper we present a detailed description of the work of Graev and the curvature estimates given by Böhm in 2004.
期刊介绍：
This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field.
The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.
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