Q曲率的全息公式
Holographic formula for Q-curvature
摘要：
本文导出了偶数维共形几何中Branson Q曲率的一个显式公式。公式中的成分来自一个更高维度的庞加莱度规;因此该公式被称为全息。当专门用于共形平坦的情况时，全息公式将Q曲率表示为Pfweian的倍数和自然一形式的发散。本文还概述了Q曲率的全息公式与第二作者提出的共形协变微分算子族的新理论之间的关系。
英文摘要：
This paper derives an explicit formula for Branson's Q-curvature in even-dimensional conformal geometry. The ingredients in the formula come from the Poincare metric in one higher dimension; hence the formula is called holographic. When specialized to the conformally flat case, the holographic formula expresses Q-curvature as a multiple of the Pfaffian and the divergence of a natural one-form. The paper also outlines the relation between holographic formulae for Q-curvature and a new theory of conformally covariant families of differential operators due to the second author.
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