Journal of Differential Geometry

On the Complex Structure of Kähler Manifolds with Nonnegative Curvature

Albert Chau and Luen-Fai Tam

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

First available in Project Euclid: 27 April 2006

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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.

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