Covering manifolds for analytic families of leaves of foliations by analytic curves
The author proves the existence of a covering manifold for any analytic foliation with singularities of a Stein manifold and any cross-section. Then he shows that a covering manifold corresponding to a codimension one Stein cross-section for an analytic foliation by curves (with singularities) of \( {\mathbb{C}}^{n}\) (or in fact of any arbitrary Stein manifold) is itself a Stein manifold. The general problem of finding an uniformization of the fibres, analytic with respect to the parameter, is still unsolved but worth studying further. In a remark the author improves his theorem 1.
scientific article; zbMATH DE number 1270108