Journal of Differential Geometry

On the Complex Structure of Kähler Manifolds with Nonnegative Curvature

Albert Chau and Luen-Fai Tam

Full-text: Open access

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.

Article information

Source
J. Differential Geom., Volume 73, Number 3 (2006), 491-530.

Dates
First available in Project Euclid: 27 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1146169936

Digital Object Identifier
doi:10.4310/jdg/1146169936

Mathematical Reviews number (MathSciNet)
MR2228320

Zentralblatt MATH identifier
1161.53351

Citation

Chau, Albert; Tam, Luen-Fai. On the Complex Structure of Kähler Manifolds with Nonnegative Curvature. J. Differential Geom. 73 (2006), no. 3, 491--530. doi:10.4310/jdg/1146169936. https://projecteuclid.org/euclid.jdg/1146169936


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