负缩紧完全Kähler流形上的不变度量

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2017-11-26 DOI:10.1090/jams/933

Damin Wu, S. Yau

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引用次数: 36

摘要

我们证明了一个全纯曲率在两个负常数之间的完备Kähler流形允许一个唯一的完备Káhler-Einstein度量。我们还证明了这个度量和Kobayashi-Royden度量都一致等价于背景Kähler度量。此外，如果完整的Kähler流形是简单连接的，并且截面曲率在两个负常数之间，则所有三个度量都被证明一致等价于Berg-man度量。特别是，我们证实了林和吴在1979年发表的两个猜想。

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Invariant metrics on negatively pinched complete Kähler manifolds

We prove that a complete Kähler manifold with holomorphic curvature bounded between two negative constants admits a unique complete Kähler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly equivalent to the background Kähler metric. Furthermore, all three metrics are shown to be uniformly equivalent to the Berg- man metric, if the complete Kähler manifold is simply-connected, with the sectional curvature bounded between two negative constants. In particular, we confirm two conjectures of R. E. Greene and H. Wu posted in 1979.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.