ON SINGULAR REAL ANALYTIC LEVI-FLAT FOLIATIONS

被引：0

作者：

Fernandez-Perez, Arturo ^{[1
]}

Mol, Rogerio ^{[1
]}

Rosas, Rudy ^{[2
]}

机构：

[1] Univ Fed Minas Gerais, Dept Matemat, Av Antonio Carlos 6627,CP 702, BR-30123970 Belo Horizonte, MG, Brazil

[2] Pontificia Univ Catolica Peru, Av Univ 1801, Lima, Peru

来源：

ASIAN JOURNAL OF MATHEMATICS | 2020年 / 24卷 / 06期

关键词：

Holomorphic foliation; CR-manifold; Levi-flat variety; HYPERSURFACES; INVARIANTS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A singular real analytic foliation F of real codimension one on an n-dimensional complex manifold M is Levi-flat if each of its leaves is foliated by immersed complex manifolds of dimension n - 1. These complex manifolds are leaves of a singular real analytic foliation G which is tangent to F. In this article, we classify germs of Levi-flat foliations at (C-n, 0) under the hypothesis that G is a germ of holomorphic foliation. Essentially, we prove that there are two possibilities for G, from which the classification of .F derives: either it has a meromorphic first integral or it is defined by a closed rational 1-form. Our local results also allow us to classify real algebraic Levi-flat foliations on the complex projective space P-n = P-C(n).

引用

页码：1007 / 1028

页数：22