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

Alcides Lins Neto

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 4, page 1369-1385
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Neto, Alcides Lins. "A note on projective Levi flats and minimal sets of algebraic foliations." Annales de l'institut Fourier 49.4 (1999): 1369-1385. <http://eudml.org/doc/75385>.

@article{Neto1999,
abstract = {In this paper we prove that holomorphic codimension one singular foliations on $\{\Bbb C\}\{\Bbb P\}^n,\; n\ge 3$ have no non trivial minimal sets. We prove also that for $n\ge 3$, there is no real analytic Levi flat hypersurface in $\{\Bbb C\}\{\Bbb P\}^n$.},
author = {Neto, Alcides Lins},
journal = {Annales de l'institut Fourier},
keywords = {nontrivial minimal set; Levi flat; singular holomorphic foliation; nontrivial minimal sets; Levi flats},
language = {eng},
number = {4},
pages = {1369-1385},
publisher = {Association des Annales de l'Institut Fourier},
title = {A note on projective Levi flats and minimal sets of algebraic foliations},
url = {http://eudml.org/doc/75385},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Neto, Alcides Lins
TI - A note on projective Levi flats and minimal sets of algebraic foliations
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1369
EP - 1385
AB - In this paper we prove that holomorphic codimension one singular foliations on ${\Bbb C}{\Bbb P}^n,\; n\ge 3$ have no non trivial minimal sets. We prove also that for $n\ge 3$, there is no real analytic Levi flat hypersurface in ${\Bbb C}{\Bbb P}^n$.
LA - eng
KW - nontrivial minimal set; Levi flat; singular holomorphic foliation; nontrivial minimal sets; Levi flats
UR - http://eudml.org/doc/75385
ER -

References

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  13. [Sm] S. SMALE, On gradient dynamical systems, Ann. of Math., 74 (1961). Zbl0136.43702
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