|
Leafwise holomorphic functions
Author(s):
R.
Feres;
A.
Zeghib
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1717-1725.
MSC (2000):
Primary 37C85;
Secondary 32A99
Posted:
January 15, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the setting of holomorphically foliated spaces.
References:
-
- 1.
- N. A'Campo and M. Burger. Réseaux arithmétiques et commensurateur d'après G. A. Margulis, Invent. Math. 116 (1994) 1-25. MR 96a:22019
- 2.
- A. Candel. The Harmonic measures of Lucy Garnett, preprint, 2000.
- 3.
- A. Candel and L. Conlon. Foliations I, Graduate Studies in Mathematics, Volume 23, AMS, 2000. MR 2002f:57058
- 4.
- D. Cerveau, E. Ghys, N. Sibony, J.C. Yoccoz. Dynamique et Géométrie Complexes, Panoramas et Synthèses, Société Mathématique de France, 1999. MR 2001a:37002
- 5.
- A. Connes. A survey of foliations and operator algebras, Proc. Symp. Pure Math., Amer. Math. Soc. (1982) 521-628. MR 84m:58140
- 6.
- L. Garnett. Foliations, the ergodic theorem and Brownian motion, J. Funct. Anal. 51 (1983), 285-311. MR 84j:58099
- 7.
- E. Ghys and P. de la Harpe. Sur les Groups Hyperboliques d'après Mikhael Gromov, Progress in Mathematics 83, Birkhäuser, Basel, 1990. MR 92f:53050
- 8.
- P. Griffiths and J. Harris. Principles of Algebraic Geometry, John Wiley & Sons, 1994. MR 95d:14001
- 9.
- A. Haefliger. Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa 16 (1962) 367-397. MR 32:6487
- 10.
- G. Hector and U. Hirsch. Introduction to the Geometric Theory of Foliations, Aspects of Mathematics, 1983, Vieweg. MR 85f:57016
- 11.
- K. Kodaira. Complex Manifolds and Deformations of Complex Structures, Springer, 1986. MR 87d:32040
- 12.
- G. A. Margulis. Discrete Subgroups of Semisimple Lie Groups, Springer, 1989.
- 13.
- Pierre Molino. Riemannian Foliations, Birkhäuser, 1987. MR 89b:53054
- 14.
- A. S. Rapinchuk, V. V. Benyash-Krivetz, V. I. Chernousov. Representation varieties of the fundamental groups of compact orientable surfaces, Israel J. Math. 93 (1996) 29-71. MR 98a:57002
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
37C85,
32A99
Retrieve articles in all Journals with MSC
(2000):
37C85,
32A99
Additional Information:
R.
Feres
Affiliation:
Department of Mathematics---1146, Washington University, St. Louis, Missouri 63130
A.
Zeghib
Affiliation:
UMPA - École Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France
DOI:
10.1090/S0002-9939-03-06909-0
PII:
S 0002-9939(03)06909-0
Keywords:
Foliated spaces,
leafwise holomorphic functions
Received by editor(s):
July 14, 2001
Posted:
January 15, 2003
Communicated by:
Michael Handel
Copyright of article:
Copyright
2003,
American Mathematical Society
|