Ricci flatness of asymptotically locally Euclidean metrics
Ricci flatness of asymptotically locally Euclidean metrics
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DOI：
10.1090/s0002-9947-02-03242-7
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发表时间：
2002-12
影响因子：
1.3
通讯作者：
Lei Ni;Yuguang Shi;Luen-Fai Tam
中科院分区：
文献类型：
--
作者：
Lei Ni;Yuguang Shi;Luen-Fai Tam
本文研究了渐近局部欧氏（ALE）Kahler流形的度量性质和函数理论。特别地，我们证明了Ricci平坦性的假设下，这种流形的Ricci曲率是非负或非正的。这个结果推广了格林和吴、莫、萧、丘等人建立的间隙型定理，也可以看作是一般的正质量型结果.该方法还证明了这类流形上多重次调和函数的Liouville性质。利用无穷远锥的结构，给出了具有非负Ricci曲率的ALE Kahler流形的Ricci平坦性的一个刻画。
In this article we study the metric property and the function theory of asymptotically locally Euclidean (ALE) Kahler manifolds. In particular, we prove the Ricci flatness under the assumption that the Ricci curvature of such manifolds is either nonnegative or nonpositive. The result provides a generalization of previous gap type theorems established by Greene and Wu, Mok, Siu and Yau, etc. It can also be thought of as a general positive mass type result. The method also proves the Liouville properties of plurisubharmonic functions on such manifolds. We also give a characterization of Ricci flatness of an ALE Kahler manifold with nonnegative Ricci curvature in terms of the structure of its cone at infinity.