Mathematische Annalen

, Volume 327, Issue 1, pp 1–23 | Cite as

On complete noncompact Kähler manifolds with positive bisectional curvature

  • Bing-Long Chen
  • Xi-Ping Zhu


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 C n and we show that the manifold is topologically R 2 n . In particular, when M n is a Kähler surface of positive bisectional curvature satisfying certain natural geometric growth conditions, it is biholomorphic to C 2.


Manifold Ricci Curvature Ahler Manifold Pseudoconvex Domain Geodesic Ball 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Bing-Long Chen
    • 1
  • Xi-Ping Zhu
    • 1
  1. 1.Department of MathematicsZhongshan UniversityGuangzhouP. R. China

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