齐次爱因斯坦度量与蝴蝶

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-06-02 DOI:10.1007/s10455-023-09905-0

Christoph Böhm, Megan M. Kerr

{"title":"齐次爱因斯坦度量与蝴蝶","authors":"Christoph Böhm, Megan M. Kerr","doi":"10.1007/s10455-023-09905-0","DOIUrl":null,"url":null,"abstract":"<div>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.\n</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":"{\"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>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.\\n</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}","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

摘要

2012年，M.M.Graev将紧齐次空间G/H关联为神经（｛\text{X｝｝_｛G/H｝），其非压缩性意味着G/H上存在G不变的爱因斯坦度量。神经（｛\text｛X｝｝_｛G/H｝）是一个紧的半代数集，在理论上由中间子群定义为纯李。在本文中，我们详细描述了Graev的工作和Böhm在2004年给出的曲率估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Homogeneous Einstein metrics and butterflies

查看原文本刊更多论文

Homogeneous Einstein metrics and butterflies

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

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.