On the Steinness of a class of Kähler manifolds

Abstract

Let $(M^n,g)$ be a complete non-compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. We prove that $M$ is holomorphically covered by a pseudoconvex domain in $\C^n$ which is homeomorphic to ${\mathbb{R}}^{2n}$, provided $(M^n,g)$ has uniform linear average quadratic curvature decay.

Theorem 1.1 has been improved, a new Theorem (Theorem 6.1) has been added