{"title":"论流形边界上具有奇点的列维平坦超曲面","authors":"Arturo Fernández-Pérez, Gustavo Marra","doi":"10.1002/mana.202300343","DOIUrl":null,"url":null,"abstract":"<p>We study germs of real-analytic Levi-flat hypersurfaces with singularities on a boundary manifold. We prove the existence of a normal form for a real-analytic Levi-flat hypersurface which is defined by the vanishing of the real part of <span></span><math>\n <semantics>\n <msub>\n <mi>B</mi>\n <mi>k</mi>\n </msub>\n <annotation>$B_k$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <msub>\n <mi>C</mi>\n <mi>k</mi>\n </msub>\n <annotation>$C_k$</annotation>\n </semantics></math>, and <span></span><math>\n <semantics>\n <msub>\n <mi>F</mi>\n <mn>4</mn>\n </msub>\n <annotation>$F_4$</annotation>\n </semantics></math> singularities. Finally, we prove a version of Morse–Vey's lemma for a real-analytic Levi-flat hypersurface with singularities on the boundary.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Levi-flat hypersurfaces with singularities on a manifold boundary\",\"authors\":\"Arturo Fernández-Pérez, Gustavo Marra\",\"doi\":\"10.1002/mana.202300343\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study germs of real-analytic Levi-flat hypersurfaces with singularities on a boundary manifold. We prove the existence of a normal form for a real-analytic Levi-flat hypersurface which is defined by the vanishing of the real part of <span></span><math>\\n <semantics>\\n <msub>\\n <mi>B</mi>\\n <mi>k</mi>\\n </msub>\\n <annotation>$B_k$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <msub>\\n <mi>C</mi>\\n <mi>k</mi>\\n </msub>\\n <annotation>$C_k$</annotation>\\n </semantics></math>, and <span></span><math>\\n <semantics>\\n <msub>\\n <mi>F</mi>\\n <mn>4</mn>\\n </msub>\\n <annotation>$F_4$</annotation>\\n </semantics></math> singularities. Finally, we prove a version of Morse–Vey's lemma for a real-analytic Levi-flat hypersurface with singularities on the boundary.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300343\",\"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://onlinelibrary.wiley.com/doi/10.1002/mana.202300343","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Levi-flat hypersurfaces with singularities on a manifold boundary
We study germs of real-analytic Levi-flat hypersurfaces with singularities on a boundary manifold. We prove the existence of a normal form for a real-analytic Levi-flat hypersurface which is defined by the vanishing of the real part of , , and singularities. Finally, we prove a version of Morse–Vey's lemma for a real-analytic Levi-flat hypersurface with singularities on the boundary.
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