{"title":"Geometry associated with the SL(3,R) action on homogeneous space using the Erlangen program","authors":"D. Biswas, Ipsita Rajwar","doi":"10.52737/18291163-2022.14.11-1-15","DOIUrl":null,"url":null,"abstract":"We investigate the action of the Lie group SL(3,R) on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of SL(3,R) are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2022.14.11-1-15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We investigate the action of the Lie group SL(3,R) on the two-dimensional homogeneous space. All the one-parameter subgroups (up to conjugacy) of SL(3,R) are considered. We discuss the orbits and curvatures of these one-parameter subgroups. We also classify these subgroups in terms of fixed points.
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