{"title":"Möbius基团的伪共形作用","authors":"M. Belraouti , M. Deffaf , Y. Raffed , A. Zeghib","doi":"10.1016/j.difgeo.2023.102070","DOIUrl":null,"url":null,"abstract":"<div><p>We study compact connected pseudo-Riemannian manifolds <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> on which the conformal group <span><math><mi>Conf</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of <span><math><mi>Conf</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is the Möbius group, then <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is conformally flat.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Pseudo-Conformal actions of the Möbius group\",\"authors\":\"M. Belraouti , M. Deffaf , Y. Raffed , A. Zeghib\",\"doi\":\"10.1016/j.difgeo.2023.102070\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study compact connected pseudo-Riemannian manifolds <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> on which the conformal group <span><math><mi>Conf</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of <span><math><mi>Conf</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is the Möbius group, then <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> is conformally flat.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-10-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224523000967\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523000967","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study compact connected pseudo-Riemannian manifolds on which the conformal group acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of is the Möbius group, then is conformally flat.
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