Leafwise holomorphic functions

Feres, R.; Zeghib, A.

doi:10.1090/S0002-9939-03-06909-0

Leafwise holomorphic functions
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by R. Feres and A. Zeghib PDF

Proc. Amer. Math. Soc. 131 (2003), 1717-1725 Request permission

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

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, DOI 10.1007/BF01231555
A. Candel. The Harmonic measures of Lucy Garnett, preprint, 2000.
Alberto Candel and Lawrence Conlon, Foliations. I, Graduate Studies in Mathematics, vol. 23, American Mathematical Society, Providence, RI, 2000. MR 1732868, DOI 10.1090/gsm/023
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
A. Connes, A survey of foliations and operator algebras, Operator algebras and applications, Part 1 (Kingston, Ont., 1980) Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, R.I., 1982, pp. 521–628. MR 679730
Lucy Garnett, Foliations, the ergodic theorem and Brownian motion, J. Functional Analysis 51 (1983), no. 3, 285–311. MR 703080, DOI 10.1016/0022-1236(83)90015-0
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, DOI 10.1007/978-1-4684-9167-8
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, DOI 10.1002/9781118032527
André Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 16 (1962), 367–397 (French). MR 189060
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, DOI 10.1007/978-3-322-85619-7
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, DOI 10.1007/978-1-4613-8590-5
G. A. Margulis. Discrete Subgroups of Semisimple Lie Groups, Springer, 1989.
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, DOI 10.1007/978-1-4684-8670-4
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, DOI 10.1007/BF02761093