On the complex structure of Kähler manifolds with nonnegative curvature. (English) Zbl 1161.53351

Summary: 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 \(\mathbb{C}^n\). 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.


53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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