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

##### MSC:
 57R30 Foliations in differential topology; geometric theory 58J65 Diffusion processes and stochastic analysis on manifolds
##### Keywords:
foliation; manifold; transversely holomorphic; holonomy
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