{"title":"紧凑同质 Leviflat CR-manifolds。","authors":"A R Al-Abdallah, B Gilligan","doi":"10.1007/s40627-021-00083-y","DOIUrl":null,"url":null,"abstract":"<p><p>We consider compact Leviflat homogeneous Cauchy-Riemann (CR) manifolds. In this setting, the Levi-foliation exists and we show that all its leaves are homogeneous and biholomorphic. We analyze separately the structure of orbits in complex projective spaces and parallelizable homogeneous CR-manifolds in our context and then combine the projective and parallelizable cases. In codimensions one and two, we also give a classification.</p>","PeriodicalId":87237,"journal":{"name":"Complex analysis and its synergies","volume":"7 3-4","pages":"25"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550170/pdf/","citationCount":"0","resultStr":"{\"title\":\"Compact homogeneous Leviflat CR-manifolds.\",\"authors\":\"A R Al-Abdallah, B Gilligan\",\"doi\":\"10.1007/s40627-021-00083-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We consider compact Leviflat homogeneous Cauchy-Riemann (CR) manifolds. In this setting, the Levi-foliation exists and we show that all its leaves are homogeneous and biholomorphic. We analyze separately the structure of orbits in complex projective spaces and parallelizable homogeneous CR-manifolds in our context and then combine the projective and parallelizable cases. In codimensions one and two, we also give a classification.</p>\",\"PeriodicalId\":87237,\"journal\":{\"name\":\"Complex analysis and its synergies\",\"volume\":\"7 3-4\",\"pages\":\"25\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550170/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex analysis and its synergies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s40627-021-00083-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2021/7/15 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex analysis and its synergies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40627-021-00083-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/7/15 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
We consider compact Leviflat homogeneous Cauchy-Riemann (CR) manifolds. In this setting, the Levi-foliation exists and we show that all its leaves are homogeneous and biholomorphic. We analyze separately the structure of orbits in complex projective spaces and parallelizable homogeneous CR-manifolds in our context and then combine the projective and parallelizable cases. In codimensions one and two, we also give a classification.
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