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

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}${}^2$.