On singular real analytic Levi-flat foliations
| Autor: | Rogério Mol, Rudy Rosas, Arturo Fernández-Pérez |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Complex Variables
Mathematics::Complex Variables Applied Mathematics General Mathematics Complex projective space Dimension (graph theory) Holomorphic function 37F75 32S65 32V40 Codimension Dynamical Systems (math.DS) Combinatorics Foliation (geology) FOS: Mathematics CR manifold Mathematics::Differential Geometry Mathematics - Dynamical Systems Complex manifold Complex Variables (math.CV) Mathematics::Symplectic Geometry Meromorphic function Mathematics |
| DOI: | 10.48550/arxiv.1808.01833 |
| Popis: | A singular real analytic foliation $\mathcal{F}$ 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 $\mathcal{L}$ which is tangent to $\mathcal{F}$. In this article, we classify germs of Levi-flat foliations at $(\mathbb{C}^{n},0)$ under the hypothesis that $\mathcal{L}$ is a germ holomorphic foliation. Essentially, we prove that there are two possibilities for $\mathcal{L}$, from which the classification of $\mathcal{F}$ derives: either it has a meromorphic first integral or 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 $\mathbb{P}^{n} = \mathbb{P}^{n}_{\mathbb{C}}$. Comment: 22 pages |
| Databáze: | OpenAIRE |
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