On the complex structure of Kähler manifolds with nonnegative curvature

Albert Chau; Luen-Fai Tam

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On the complex structure of Kähler manifolds with nonnegative curvature

Albert Chau·Luen-Fai Tam

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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 bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space $\C^n$. We also show that the volume growth condition can be removed if we assume $(M, g)$ has average quadratic scalar curvature decay (see Theorem 2.1) and positive curvature operator.

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Albert Chau, Luen-Fai Tam. 2005-08-29. On the complex structure of Kähler manifolds with nonnegative curvature. https://arxiv.org/abs/math/0504422

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