A global stability theorem for transversely holomorphic foliations. (English) Zbl 0876.57040

Brunella, Marco

Ann. Global Anal. Geom. 15, No. 2, 179-186 (1997).

A foliation \(\mathcal F\) of complex codimension one on a manifold \(M\) is said to be transversely holomorphic if it is given by a collection of submersions onto open subsets of \(\mathbb{C}\) so that the transition functions are holomorphic. It is shown that if \(M\) is compact and connected and \(\mathcal F\) is such a foliation and \(\mathcal F\) has a compact leaf of finite holonomy then every leaf is compact and has finite holonomy.

Reviewer: D.B.Gauld (Auckland)

MSC:

57R30	Foliations in differential topology; geometric theory
58J65	Diffusion processes and stochastic analysis on manifolds

Keywords:

foliation; manifold; transversely holomorphic; holonomy