Foliations with locally stable leaves (Q1357935)

The main theorem of the present paper is the following: Let \(\mathcal F\) be a foliation of codimension \(q\) of a manifold \(M\) with all leaves being locally stable. Then: (1) each leaf is closed in \(M\); (2) all holonomy groups of \(\mathcal F\) are finite; (3) \(M/{\mathcal F}\) is a \(q\)-dimensional smooth orbifold; (4) the union of leaves with trivial holonomy is a connected, open and dense subset \(T\) of \(M\) which is a locally trivial bundle over the manifold \(T/{\mathcal F}\); (5) for each leaf \(L\in{\mathcal F}\), there exists a natural holonomic covering of \(L\) by a leaf \(L_0\) with trivial holonomy group.