Displaying similar documents to “Levi-Flat submanifolds and holomorphic extension of foliations”

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

Takashi Inaba (1992)

Collectanea Mathematica

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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.

On the smoothness of Levi-foliations.

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

Publicacions Matemàtiques

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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

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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

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