A sub-product construction of Poincare-Einstein metrics
A sub-product construction of Poincare-Einstein metrics
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庞加莱-爱因斯坦度量的子积构造
DOI：
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发表时间：
2006
期刊：
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通讯作者：
Felipe Leitner
中科院分区：
文献类型：
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作者：
A. Gover;Felipe Leitner
给定任意两个Einstein（伪）度量，其标量曲率适当相关，我们给出了一个Poincare-Einstein（伪）度量的显式构造，其共形无穷大是初始度量乘积的共形类.我们表明，这些度量是等价的环境度量给定的共形结构。环境度规具有与共形完整性一致的完整性。在一般情况下，环境度规直接产生为原始爱因斯坦空间上的度规锥的乘积。一般来说，我们构造的庞加莱度规的共形无穷大不是爱因斯坦度规，因此这描述了一类非共形爱因斯坦度规，其中（Fefferman-Graham）阻碍张量为零。
Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincare–Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincare metric we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman–Graham) obstruction tensor vanishes.