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International Journal of Differential Equations
Volume 2012 (2012), Article ID 585298, 6 pages
http://dx.doi.org/10.1155/2012/585298
Research Article

A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations

Instituto de Matematica, Universidade Federal do Rio de Janeiro, CP 68530, 21945-970, Rio de Janeiro, RJ, Brazil

Received 22 May 2012; Accepted 22 July 2012

Academic Editor: Kanishka Perera

Copyright © 2012 Bruno Scardua. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that a transversely holomorphic foliation, which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not a zero measure subset. Similarly, we prove that a finitely generated subgroup of holomorphic diffeomorphisms of a connected complex manifold is finite provided that the set of periodic orbits is not a zero measure subset.