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

Chau, Albert; Tam, Luen-Fai

J. Differ. Geom. 73, No. 3, 491-530 (2006).

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.

MSC:

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