{"title":"Compact geodesic orbit spaces with a simple isotropy group","authors":"Z. Chen, Y. Nikolayevsky, Yu Nikonorov","doi":"10.1007/s10455-022-09877-7","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span>\\(M=G/H\\)</span> be a compact, simply connected, Riemannian homogeneous space, where <i>G</i> is (almost) effective and <i>H</i> is a <i>simple</i> Lie group. In this paper, we first classify all <i>G</i>-naturally reductive metrics on <i>M</i>, and then all <i>G</i>-geodesic orbit metrics on <i>M</i>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"63 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-022-09877-7.pdf","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Global Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-022-09877-7","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: 6
Abstract
Let \(M=G/H\) be a compact, simply connected, Riemannian homogeneous space, where G is (almost) effective and H is a simple Lie group. In this paper, we first classify all G-naturally reductive metrics on M, and then all G-geodesic orbit metrics on M.
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.