New Einstein Metrics in Dimension Five
New Einstein Metrics in Dimension Five
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DOI：
10.4310/jdg/1090348129
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发表时间：
2000-03
影响因子：
2.5
通讯作者：
C. Boyer;K. Galicki
中科院分区：
文献类型：
--
作者：
C. Boyer;K. Galicki
本文的目的是介绍一种新的方法来证明某些单连通奇维流形上Sasakian-Einstein度量的存在性。然后我们应用这种方法证明了$\scriptstyle{S^2\times S^3}$和$\scriptstyle{（S^2\times S^3）#（S^2\times S^3）}上新的Sasakian-Einstein度量的存在性。这些给出了第一个已知的非正则的Sasakian-Einstein 5-流形的例子。我们的方法包括将Sasakian-Einstein结构描述为某些孤立超曲面奇点的链接，并利用Demailly和Kollar，AG/9910118的最近工作，他们获得了具有商奇点的Kahler-Einstein del Pezzo曲面的新例子。
The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on $\scriptstyle{S^2\times S^3}$ and on $\scriptstyle{(S^2\times S^3)# (S^2\times S^3).}$ These give the first known examples of non-regular Sasakian-Einstein 5-manifolds. Our method involves describing the Sasakian-Einstein structures as links of certain isolated hypersurface singularities, and makes use of the recent work of Demailly and Koll\'ar, AG/9910118, who obtained new examples of K\"ahler-Einstein del Pezzo surfaces with quotient singularities.