{"title":"CR 向量束截面的正则性","authors":"B. Lamel, N. Mir","doi":"10.1090/bproc/149","DOIUrl":null,"url":null,"abstract":"<p>In this note, we show that every generalized section <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sigma\">\n <mml:semantics>\n <mml:mi>σ<!-- σ --></mml:mi>\n <mml:annotation encoding=\"application/x-tex\">\\sigma</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> of a CR vector bundle <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\">\n <mml:semantics>\n <mml:mi>E</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">E</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> over a CR manifold <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M\">\n <mml:semantics>\n <mml:mi>M</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">M</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> has the property that near most points of its singular support, there exists a proper abstract CR subbundle <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F subset-of upper E\">\n <mml:semantics>\n <mml:mrow>\n <mml:mi>F</mml:mi>\n <mml:mo>⊂<!-- ⊂ --></mml:mo>\n <mml:mi>E</mml:mi>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">F \\subset E</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> which has the property that every <italic>real</italic> subbundle of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\">\n <mml:semantics>\n <mml:mi>E</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">E</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> which contains the image of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sigma\">\n <mml:semantics>\n <mml:mi>σ<!-- σ --></mml:mi>\n <mml:annotation encoding=\"application/x-tex\">\\sigma</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> also contains <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\n <mml:semantics>\n <mml:mi>F</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"33 S1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularity of sections of CR vector bundles\",\"authors\":\"B. Lamel, N. Mir\",\"doi\":\"10.1090/bproc/149\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this note, we show that every generalized section <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"sigma\\\">\\n <mml:semantics>\\n <mml:mi>σ<!-- σ --></mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\sigma</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> of a CR vector bundle <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E\\\">\\n <mml:semantics>\\n <mml:mi>E</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">E</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> over a CR manifold <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper M\\\">\\n <mml:semantics>\\n <mml:mi>M</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">M</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> has the property that near most points of its singular support, there exists a proper abstract CR subbundle <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F subset-of upper E\\\">\\n <mml:semantics>\\n <mml:mrow>\\n <mml:mi>F</mml:mi>\\n <mml:mo>⊂<!-- ⊂ --></mml:mo>\\n <mml:mi>E</mml:mi>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">F \\\\subset E</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> which has the property that every <italic>real</italic> subbundle of <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E\\\">\\n <mml:semantics>\\n <mml:mi>E</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">E</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> which contains the image of <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"sigma\\\">\\n <mml:semantics>\\n <mml:mi>σ<!-- σ --></mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">\\\\sigma</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> also contains <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper F\\\">\\n <mml:semantics>\\n <mml:mi>F</mml:mi>\\n <mml:annotation encoding=\\\"application/x-tex\\\">F</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula>.</p>\",\"PeriodicalId\":106316,\"journal\":{\"name\":\"Proceedings of the American Mathematical Society, Series B\",\"volume\":\"33 S1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the American Mathematical Society, Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/bproc/149\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/149","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在本注释中，我们证明了在 CR 流形 M M 上 CR 向量束 E E 的每个广义截面 σ \sigma 都具有这样的性质：在其奇异支持的大部分点附近，存在一个适当的抽象 CR 子束带 F ⊂ E F \subset E，它具有这样的性质：E E 的每个包含 σ \sigma 的像的实子束带也包含 F F。
In this note, we show that every generalized section σ\sigma of a CR vector bundle EE over a CR manifold MM has the property that near most points of its singular support, there exists a proper abstract CR subbundle F⊂EF \subset E which has the property that every real subbundle of EE which contains the image of σ\sigma also contains FF.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
