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arXiv 0908.1430math.DGmath-phmath.MP
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共形紧Einstein流形的构造

Construction of Conformally Compact Einstein Manifolds

Dezhong Chen

摘要:

我们给出了共形紧Einstein流形的一些显式例子,它们的共形紧化是由闭Einstein流形与Kahler-Einstein流形乘积上的主圆丛的全空间的黎曼乘积所划分的.我们计算相关的共形不变量,即,偶数维的重整化体积和奇数维的共形反常。作为副产品,我们得到了一些黎曼积与消失的Q-曲率。

英文摘要:

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in odd dimensions. As a by-product, we obtain some Riemannian products with vanishing Q-curvature.

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