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July 2006 On the Complex Structure of Kähler Manifolds with Nonnegative Curvature
Albert Chau, Luen-Fai Tam
J. Differential Geom. 73(3): 491-530 (July 2006). DOI: 10.4310/jdg/1146169936

Abstract

We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative and bounded holomorphic bi-sectional curvature and maximal volume growth is biholomorphic to complex Euclidean space Cn. We also show that the volume growth condition can be removed if we assume the Kähler manifold has average quadratic scalar curvature decay and positive curvature operator.

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Albert Chau. Luen-Fai Tam. "On the Complex Structure of Kähler Manifolds with Nonnegative Curvature." J. Differential Geom. 73 (3) 491 - 530, July 2006. https://doi.org/10.4310/jdg/1146169936

Information

Published: July 2006
First available in Project Euclid: 27 April 2006

zbMATH: 1161.53351
MathSciNet: MR2228320
Digital Object Identifier: 10.4310/jdg/1146169936

Rights: Copyright © 2006 Lehigh University

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Vol.73 • No. 3 • July 2006
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