Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Leafwise holomorphic functions


Authors: R. Feres and A. Zeghib
Journal: Proc. Amer. Math. Soc. 131 (2003), 1717-1725
MSC (2000): Primary 37C85; Secondary 32A99
Published electronically: January 15, 2003
MathSciNet review: 1955258
Full-text PDF Free Access

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 [Enhancements On Off] (What's this?)

  • 1. Norbert A’Campo and Marc Burger, Réseaux arithmétiques et commensurateur d’après G. A. Margulis, Invent. Math. 116 (1994), no. 1-3, 1–25 (French). MR 1253187, 10.1007/BF01231555
  • 2. A. Candel. The Harmonic measures of Lucy Garnett, preprint, 2000.
  • 3. Alberto Candel and Lawrence Conlon, Foliations. I, Graduate Studies in Mathematics, vol. 23, American Mathematical Society, Providence, RI, 2000. MR 1732868
  • 4. Dominique Cerveau, Étienne Ghys, Nessim Sibony, and Jean-Christophe Yoccoz, Dynamique et géométrie complexes, Panoramas et Synthèses [Panoramas and Syntheses], vol. 8, Société Mathématique de France, Paris; distributed by American Mathematical Society, Providence, RI, 1999 (French). Papers from the Meeting “State of the Art of the Research of the Société Mathématique de France” held at École Normale Supérieure de Lyon, Lyon, January 1997. MR 1760840
  • 5. A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part I (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 521–628. MR 679730
  • 6. Lucy Garnett, Foliations, the ergodic theorem and Brownian motion, J. Funct. Anal. 51 (1983), no. 3, 285–311. MR 703080, 10.1016/0022-1236(83)90015-0
  • 7. É. Ghys and P. de la Harpe (eds.), Sur les groupes hyperboliques d’après Mikhael Gromov, Progress in Mathematics, vol. 83, Birkhäuser Boston, Inc., Boston, MA, 1990 (French). Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988. MR 1086648
  • 8. Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1994. Reprint of the 1978 original. MR 1288523
  • 9. André Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa (3) 16 (1962), 367–397 (French). MR 0189060
  • 10. Gilbert Hector and Ulrich Hirsch, Introduction to the geometry of foliations. Part B. Foliations of codimension one, Aspects of Mathematics, E3, Friedr. Vieweg & Sohn, Braunschweig, 1983. MR 726931
  • 11. Kunihiko Kodaira, Complex manifolds and deformation of complex structures, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 283, Springer-Verlag, New York, 1986. Translated from the Japanese by Kazuo Akao; With an appendix by Daisuke Fujiwara. MR 815922
  • 12. G. A. Margulis. Discrete Subgroups of Semisimple Lie Groups, Springer, 1989.
  • 13. Pierre Molino, Riemannian foliations, Progress in Mathematics, vol. 73, Birkhäuser Boston, Inc., Boston, MA, 1988. Translated from the French by Grant Cairns; With appendices by Cairns, Y. Carrière, É. Ghys, E. Salem and V. Sergiescu. MR 932463
  • 14. A. S. Rapinchuk, V. V. Benyash-Krivetz, and V. I. Chernousov, Representation varieties of the fundamental groups of compact orientable surfaces, Israel J. Math. 93 (1996), 29–71. MR 1380633, 10.1007/BF02761093

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: http://dx.doi.org/10.1090/S0002-9939-03-06909-0
Keywords: Foliated spaces, leafwise holomorphic functions
Received by editor(s): July 14, 2001
Published electronically: January 15, 2003
Communicated by: Michael Handel
Article copyright: © Copyright 2003 American Mathematical Society