In this paper we prove that holomorphic codimension one singular foliations on have no non trivial minimal sets. We prove also that for , there is no real analytic Levi flat hypersurface in .
Dans cet article on démontre qu’un feuilletage holomorphe de codimension un dans , n’a pas de minimaux non triviaux. On démontre aussi que pour , il n’existe pas de surfaces de Levi plates, analytiques réelles, dans .
@article{AIF_1999__49_4_1369_0,
author = {Neto, Alcides Lins},
title = {A note on projective {Levi} flats and minimal sets of algebraic foliations},
journal = {Annales de l'Institut Fourier},
pages = {1369--1385},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {49},
number = {4},
year = {1999},
doi = {10.5802/aif.1721},
zbl = {0963.32022},
mrnumber = {2000h:32047},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1721/}
}
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 SP - 1369 EP - 1385 VL - 49 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1721/ DO - 10.5802/aif.1721 LA - en ID - AIF_1999__49_4_1369_0 ER -
%0 Journal Article %A Neto, Alcides Lins %T A note on projective Levi flats and minimal sets of algebraic foliations %J Annales de l'Institut Fourier %D 1999 %P 1369-1385 %V 49 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1721/ %R 10.5802/aif.1721 %G en %F AIF_1999__49_4_1369_0
Neto, Alcides Lins. A note on projective Levi flats and minimal sets of algebraic foliations. Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1369-1385. doi: 10.5802/aif.1721
[AL-N] , Algebraic solutions of polynomial differential equations and foliations in dimension two, Springer Lecture Notes, 1345 (1988), 192-232. | Zbl | MR
[BB] , , On the zeroes of meromorphic vector fields, Essais en l'honneur de De Rham, (1970) 29-47. | Zbl | MR
[CLS1] , and , Minimal sets of foliations on complex projective spaces, Publ. Math. IHES, 68 (1988) 187-203. | Zbl | MR | Numdam | EuDML
[CLS2] , and , Foliations with algebraic limit sets, Ann. of Math., 135 (1992) 429-446. | Zbl | MR
[E] , Pseudo-convexité locale dans les variétés Kahlériennes, Ann. Inst. Fourier, 25-2 (1975), 295-314. | Zbl | MR | Numdam | EuDML
[G] , Lectures on Algebraic Topology, W. A. Benjamin inc., 1967. | Zbl | MR
[H] , Differential Topology, Springer Verlag, N.Y., 1976. | Zbl
[Ha] , Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, serie 3, vol. 16 (1962), 367-397. | Zbl | MR | Numdam | EuDML
[HL] and , Theory of Functions on Complex Manifolds, Birkhäuser, 1984. | Zbl
[M] , Morse Theory, Annals of Mathematics Studies 51, Princeton University Press, 1963. | Zbl
[MB] , Some remarks on indices of holomorphic vector fields, Prépublication 97, Université de Bourgogne (1996). | Zbl
[S] , Techniques of extension of analytic objects, Marcel Dekker Inc., New-York, 1974. | Zbl
[Sm] , On gradient dynamical systems, Ann. of Math., 74 (1961). | Zbl
[ST] and , Gap-sheaves and extension of coherent analytic subsheaves, Lect. Notes in Math., 172 (1971). | Zbl | MR
[T] , Domaines pseudo-convexes sur les variétés Kahlériennes, Jour. Math. Kyoto University, 6-3 (1967), 323-357. | Zbl | MR
[To] , Tracce delle funzioni olomorfe sulle sottovarietà analitiche reali d'una varietà complessa, Ann. Scuola Norm. Sup. Pisa, (1966), 31-43. | Zbl | MR | Numdam
Cité par Sources :



