{"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}
引用次数: 0
Abstract
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.
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。
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