Displaying similar documents to “Singular Levi-flat hypersurfaces and codimension one foliations”

On Levi-flat hypersurfaces tangent to holomorphic webs

Arturo Fernández-Pérez (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We investigate real analytic Levi-flat hypersurfaces tangent to holomorphic webs. We introduce the notion of first integrals for local webs. In particular, we prove that a k -web with finitely many invariant subvarieties through the origin tangent to a Levi-flat hypersurface has a holomorphic first integral.

On the nonexistence of CR functions on Levi-flat CR manifolds.

Takashi Inaba (1992)

Collectanea Mathematica

Similarity:

We show that no compact Levi-flat CR manifold of CR codimension one admits a continuous CR function which is nonconstant along leaves of the Levi foliation. We also prove the nonexistence of certain CR functions on a neighborhood of a compact leaf of some Levi-flat CR 3-manifolds, and apply it to showing that some foliated 3-manifolds cannot be embedded as smooth Levi-flat real hypersurfaces in complex surfaces.

Singular sets of holonomy maps for algebraic foliations

Gabriel Calsamiglia, Bertrand Deroin, Sidney Frankel, Adolfo Guillot (2013)

Journal of the European Mathematical Society

Similarity:

In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty...

On the smoothness of Levi-foliations.

D. E. Barrett, John Erik Fornaess (1988)

Publicacions Matemàtiques

Similarity:

We study the regularity of the induced foliation of a Levi-flat hypersurface in C, showing that the foliation is as many times continuously differentiable as the hypersurface itself. The key step in the proof given here is the construction of a certain family of approximate plurisubharmonic defining functions for the hypersurface in question.

A note on projective Levi flats and minimal sets of algebraic foliations

Alcides Lins Neto (1999)

Annales de l'institut Fourier

Similarity:

In this paper we prove that holomorphic codimension one singular foliations on ℂ ℙ n , n ≥ 3 have no non trivial minimal sets. We prove also that for n ≥ 3 , there is no real analytic Levi flat hypersurface in ℂ ℙ n .

Unfoldings of holomorphic foliations.

Xavier Gómez-Mont (1989)

Publicacions Matemàtiques

Similarity:

The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial.

Local embeddings of lines in singular hypersurfaces

Guangfeng Jiang, Dirk Siersma (1999)

Annales de l'institut Fourier

Similarity:

Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.