an:01218272
Zbl 0911.32022
Takayama, Shigeharu
The Levi problem and the structure theorem for non-negatively curved complete K??hler manifolds
EN
J. Reine Angew. Math. 504, 139-157 (1998).
00051454
1998
j
32E05 32T99
non-negatively curved complete K??hler manifolds; Levi problem; complex manifolds
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 K??hler version of the Cheeger-Gromoll Riemannian structure theorem: Every complete K??hler 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.
S.Takayama (Osaka)