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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.

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