Positively Curved Complete Noncompact Kähler Manifolds

Details Positively Curved Complete Noncompact Kähler Manifolds Positively Curved Complete Noncompact Kähler Manifolds

2002-11-24

arxiv.org/abs/math/0211373v1

Mathematics

Differential Geometry

33 pages

Scientific paper

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
$c_{1}(M)^{2}$ is biholomorphic to ${\C}^2$.

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