Mathematical Research Letters

Volume 2, Issue 4, July 1995 pp. 401-414.

Limits of complete holomorphic vector fields

Authors: Franc Forstneric
Author institution: University of Wisconsin

Summary: Let $V$ be a holomorphic vector field\ on a Stein manifold $M$. If $V$ can be approximated by complete \holomorphic vector field s, uniformly on compacts in $M$, we prove that the fundamental domain of $V$ is single sheeted, pseudoconvex, and it has simply connected fibers. Moreover, every complex orbit of $V$ has connectivity at most one (Theorem 1.1). We then find several explicit classes of \holomorphic vector field s on ${\Bbb C}^2$ which are not limits of complete fields (Corollaries 1.4--1.6).

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