Uniformization of the leaves of a rational vector field

Alberto Candel; X. Gómez-Mont

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 4, page 1123-1133
  • ISSN: 0373-0956

Abstract

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We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.

How to cite

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Candel, Alberto, and Gómez-Mont, X.. "Uniformization of the leaves of a rational vector field." Annales de l'institut Fourier 45.4 (1995): 1123-1133. <http://eudml.org/doc/75148>.

@article{Candel1995,
abstract = {We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.},
author = {Candel, Alberto, Gómez-Mont, X.},
journal = {Annales de l'institut Fourier},
keywords = {holomorphic foliations; uniformization},
language = {eng},
number = {4},
pages = {1123-1133},
publisher = {Association des Annales de l'Institut Fourier},
title = {Uniformization of the leaves of a rational vector field},
url = {http://eudml.org/doc/75148},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Candel, Alberto
AU - Gómez-Mont, X.
TI - Uniformization of the leaves of a rational vector field
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 4
SP - 1123
EP - 1133
AB - We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.
LA - eng
KW - holomorphic foliations; uniformization
UR - http://eudml.org/doc/75148
ER -

References

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  1. [1]L. AHLFORS, Complex Analysis, MacGraw Hill, New York, 1966. Zbl0154.31904
  2. [2]L. AHLFORS, Conformal Invariants, MacGraw Hill, New York, 1973. 
  3. [3]R. BRODY, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., 235 (1978), 213-219. Zbl0416.32013MR57 #10010
  4. [4]C. CAMACHO, A. LINS, P. SAD, Minimal sets of foliations on complex projective spaces, Publ. Math. IHES, 68 (1989), 187-203. Zbl0682.57012
  5. [5]A. CANDEL, Uniformization of surface laminations, Ann. Scient. Ec. Norm. Sup., 26 (1993), 489-516. Zbl0785.57009MR94f:57025
  6. [6]D. CERVEAU, Equations différentielles algébriques : Remarques et problèmes, J. Fac. Sci. Univ. Tokyo, 36 (1989), 665-680. Zbl0698.58047MR91b:32035
  7. [7]E. GHYS, Gauss-Bonnet Theorem for 2-dimensional foliations, J. of Funct. Anal., 77 (1988), 51-59. Zbl0656.57017MR89d:57040
  8. [8]A.A. GLUTSUK, The hyperbolicity of phase curves of a generic polynomial vector field in Cn, Functional Analysis and its applications, 28 (1994), 77-84. Zbl0848.32032
  9. [9]A. LINS, Simultaneous uniformization for the leaves of projective foliations by curves, to appear in Bol. Soc. Brasileira. Zbl0821.32027
  10. [10]C. MOORE & C. SCHOCHET, Global analysis of foliated spaces, Springer-Verlag, New York, 1988. Zbl0648.58034
  11. [11]A. VERJOVSKY, A uniformization theorem for holomorphic foliations., Contemp. Math., 58(III) (1987), 233-253. Zbl0619.32017MR88h:57027

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