Ambient metric construction of Q-curvature in conformal and CR geometries
Ambient metric construction of Q-curvature in conformal and CR geometries
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DOI：
10.4310/mrl.2003.v10.n6.a9
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发表时间：
2003-03
影响因子：
1
通讯作者：
C. Fefferman;K. Hirachi
中科院分区：
文献类型：
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作者：
C. Fefferman;K. Hirachi
我们给出了几何推导布兰森的Q-曲率的环境度量与共形结构，它自然遵循的环境度量建设共形不变的运营商，并可以应用于一大类不变的运营商。这个过程也可以应用于CR几何，并给出了一个CR模拟的Q-曲率;然后证明，Q-曲率给出了系数的对数奇异性的Szego核的3维CR流形。
We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to a large class of invariant operators. This procedure can be also applied to CR geometry and gives a CR analog of the Q-curvature; it then turns out that the Q-curvature gives the coefficient of the logarithmic singularity of the Szego kernel of 3-dimensional CR manifolds.