On Complete Noncompact Kähler Manifolds with Positive Bisectional Curvature

Details On Complete Noncompact Kähler Manifolds with Positive Bisectional Curvature On Complete Noncompact Kähler Manifolds with Positive Bisectional Curvature

2002-11-24

arxiv.org/abs/math/0211370v1

Mathematics

Differential Geometry

31 pages. To appear in Math. Ann

Scientific paper

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}$^{2}$.

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