Non-negatively curved Kähler manifolds with average quadratic curvature decay

Albert Chau; Luen-Fai Tam

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arXiv · math/0510252

Non-negatively curved Kähler manifolds with average quadratic curvature decay

Albert Chau·Luen-Fai Tam

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Abstract

Let $(M, g)$ be a complete non-compact Kähler 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 Kähler-Ricci flow with non-negative and uniformly bounded holomorphic bisectional curvature. We also classify certain local limits arising from the Kähler-Ricci flow in the absence of uniform estimates on the injectivity radius.

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BibTeX RIS

Albert Chau, Luen-Fai Tam. 2005-10-12. Non-negatively curved Kähler manifolds with average quadratic curvature decay. https://arxiv.org/abs/math/0510252

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