Non-negatively curved Kähler manifolds with average quadratic curvature decay

Details Non-negatively curved Kähler manifolds with average quadratic curvature decay Non-negatively curved Kähler manifolds with average quadratic curvature decay

2005-10-12

arxiv.org/abs/math/0510252v1

Mathematics

Differential Geometry

Scientific paper

Let $(M, g)$ be a complete non-compact K\"ahler manifold with non-negative and bounded holomorphic bisectional curvature. Extending our techniques developed in \cite{CT3}, we prove that the universal cover $\wt M$ of $M$ is biholomorphic to $\ce^n$ provided either that $(M, g)$ has average quadratic curvature decay, or $M$ supports an eternal solution to the K\"ahler-Ricci flow with non-negative and uniformly bounded holomorphic bisectional curvature. We also classify certain local limits arising from the K\"ahler-Ricci flow in the absence of uniform estimates on the injectivity radius.

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