Closed holomorphic 1-forms without zeros on Stein Manifolds

We prove that a Stein manifold admits a closed holomorphic 1-form without zeros in every class of the first cohomology group. We also prove an approximation result for closed holomorphic 1-forms without zeros defined in a neighborhood of a compact subset.
18 pages, 4 figures, to be published in Mathematische Zeitschrift