  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}$^{2}$.

Differential Geometry