{"title":"利用Erlangen程序与齐次空间上SL(3,R)作用相关的几何","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":"{\"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}","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}
Geometry associated with the SL(3,R) action on homogeneous space using the Erlangen program
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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