On the complex structure of Kähler manifolds with nonnegative curvature

Details On the complex structure of Kähler manifolds with nonnegative curvature On the complex structure of Kähler manifolds with nonnegative curvature

2005-04-21

arxiv.org/abs/math/0504422v3

Mathematics

Differential Geometry

:37 pages, references rearranged, typos corrected

Scientific paper

We study the asymptotic behavior of the K\"ahler-Ricci flow on K\"ahler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact K\"ahler 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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