Fonctions et feuilletages Levi-Flat. Étude locale

Dominique Cerveau[1]; Paulo R. Sad[2]

  • [1] Institut de Recherches Mathématiques de Rennes Université de Rennes 1 Campus de Beaulieu 35042 Rennes, France
  • [2] Instituto de Matemática Pura e Aplicada Estrada D. Castorina 110, Jardim Botânico 22320-010 Rio de Janeiro, Brasil

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 2, page 427-445
  • ISSN: 0391-173X

Abstract

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We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.

How to cite

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Cerveau, Dominique, and Sad, Paulo R.. "Fonctions et feuilletages Levi-Flat. Étude locale." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.2 (2004): 427-445. <http://eudml.org/doc/84536>.

@article{Cerveau2004,
abstract = {We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.},
affiliation = {Institut de Recherches Mathématiques de Rennes Université de Rennes 1 Campus de Beaulieu 35042 Rennes, France; Instituto de Matemática Pura e Aplicada Estrada D. Castorina 110, Jardim Botânico 22320-010 Rio de Janeiro, Brasil},
author = {Cerveau, Dominique, Sad, Paulo R.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {fre},
number = {2},
pages = {427-445},
publisher = {Scuola Normale Superiore, Pisa},
title = {Fonctions et feuilletages Levi-Flat. Étude locale},
url = {http://eudml.org/doc/84536},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Cerveau, Dominique
AU - Sad, Paulo R.
TI - Fonctions et feuilletages Levi-Flat. Étude locale
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 2
SP - 427
EP - 445
AB - We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.
LA - fre
UR - http://eudml.org/doc/84536
ER -

References

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  6. [Mal I] B. Malgrange, Frobenius avec singularités I : Codimension un, Inst. Hautes Études Sci. Publ. Math. No. 46 (1976), 163-173. Zbl0355.32013MR508169
  7. [Mal II] B. Malgrange, Frobenius avec singularités II : Le cas général, Invent. Math. 39 (1977), 67-89. Zbl0375.32012MR508170
  8. [Mo] R. Moussu, Sur l’existence d’intégrales premières pour un germe de forme de Pfaff, Ann. Inst. Fourier (Grenoble) 26 (1976), 171-220. Zbl0328.58002MR415657
  9. [Po] H. Poincaré, “Note sur les propriétés des fonctions définies par les équations différentielles”, Oeuvres t.I, XXXVI, Gauthier-Villars, 1951. 
  10. [Re] G. Reeb, “Sur certains propriétés topologiques des variétés feuilletés”, Actual. Sci. Indust., 1183, Hermann, 1952. Zbl0049.12602MR55692
  11. [Sa] K. Saito, On a generalization of de-Rham lemma, Ann. Inst. Fourier (Grenoble) 26 (1976), 165-170. Zbl0338.13009MR413155

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