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Уфимский математический журнал, 2017, том 9, выпуск 3, страницы 172–185
(Mi ufa397)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Levi-flat world: a survey of local theory
A. Sukhov Université de Lille (Sciences et Technologies),
U.F.R. de Mathématiques,
59655 Villeneuve d’Ascq, Cedex, France
Аннотация:
This expository paper concerns local properties of Levi-flat real analytic manifolds with singularities. Levi-flat manifolds arise naturally in Complex Geometry and Foliation Theory. In many cases (global) compact Levi-flat manifolds without singularities do not exist.
These global obstructions make natural the study of Levi-flat objects with singularities because they always exist. The present expository paper deals with some recent results on local geometry of Levi-flat singularities. One of the main questions concerns an extension of the Levi foliation as a holomorphic foliation to a full neighborhood of singularity. It turns out that in general such extension
does not exist. Nevertheless, the Levi foliation always extends as a holomorphic web (a foliation with branching) near a non-dicritical singularity. We also present an efficient criterion characterizing these singularities.
Ключевые слова:
CR structure, Levi-flat manifold.
Поступила в редакцию: 19.06.2017
Образец цитирования:
A. Sukhov, “Levi-flat world: a survey of local theory”, Уфимск. матем. журн., 9:3 (2017), 172–185; Ufa Math. J., 9:3 (2017), 172–185
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ufa397 https://www.mathnet.ru/rus/ufa/v9/i3/p172
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Страница аннотации: | 256 | PDF русской версии: | 174 | PDF английской версии: | 62 | Список литературы: | 35 |
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