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The Levi problem and the structure theorem for non-negatively curved complete Kähler manifolds. (English) Zbl 0911.32022
The subject of this paper is the Levi problem on complex manifolds.
The main result is: A complex manifold with a negative canonical bundle is holomorphically convex if and only if it is pseudoconvex.
The method of the proof is based on an analytic version of the so-called concentration method on the study of adjoint bundles in algebraic geometry.
As an application, one has the following Kähler version of the Cheeger-Gromoll Riemannian structure theorem: Every complete Kähler manifold with nonnegative sectional curvature and positive Ricci curvature, has a structure of holomorphic fibre bundle over a Stein manifold whose typical fibre is biholomorphic to some compact Hermitian symmetric manifold.
Reviewer: S.Takayama (Osaka)

MSC:
32E05 Holomorphically convex complex spaces, reduction theory
32T99 Pseudoconvex domains
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