On Complete Noncompact K\"{a}hler Manifolds with Positive Bisectional Curvature

Abstract

We prove that a complete noncompact K\"{a}hler manifold $M^{n}$of positive bisectional curvature satisfying suitable growth conditions is biholomorphic to a pseudoconvex domain of {\bf C}$^{n}$ and we show that the manifold is topologically {\bf R}$^{2n}$. In particular, when $M^{n}$ is a K\"{a}hler surface of positive bisectional curvature satisfying certain natural geometric growth conditions, it is biholomorphic to {\bf C}$^{2}$.