English

Positively Curved Complete Noncompact K\"{a}hler Manifolds

Differential Geometry 2007-05-23 v1

Abstract

In this paper we give a partial affirmative answer to a conjecture of Greene-Wu and Yau. We prove that a complete noncompact K\"ahler surface with positive and bounded sectional curvature and with finite analytic Chern number c1(M)2c_{1}(M)^{2} is biholomorphic to \C2{\C}^2.

Keywords

Cite

@article{arxiv.math/0211373,
  title  = {Positively Curved Complete Noncompact K\"{a}hler Manifolds},
  author = {Bing-Long Chen and Xi-Ping Zhu},
  journal= {arXiv preprint arXiv:math/0211373},
  year   = {2007}
}

Comments

33 pages

R2 v1 2026-07-22T16:49:42.465Z