Articles

POSITIVELY CURVED COMPLETE NONCOMPACT KÄHLER MANIFOLDS

  • CHEN Bing-Long ,
  • SHU Xi-Beng
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  • Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Received date: 2008-12-31

  Online published: 2009-07-20

Supported by

This work was partially supported by 973 project (2006CB805905) and NSFC (10831008)

Abstract

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. Among other things, we prove that a complete noncompact K¨ahler surface with positive and bounded sectional curvature and with finite analytic Chern number c1(M)2 is biholomorphic to C2.

Cite this article

CHEN Bing-Long , SHU Xi-Beng . POSITIVELY CURVED COMPLETE NONCOMPACT KÄHLER MANIFOLDS[J]. Acta mathematica scientia, Series B, 2009 , 29(4) : 829 -845 . DOI: 10.1016/S0252-9602(09)60073-4

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