On Complete Noncompact Kähler Manifolds with Positive Bisectional Curvature

Abstract

We prove that a complete noncompact Kähler 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 Kähler surface of positive bisectional curvature satisfying certain natural geometric growth conditions, it is biholomorphic to {\bf C}${}^2$.

31 pages. To appear in Math. Ann