Ambient metric construction of Q-curvature in conformal and CR geometries

Details Ambient metric construction of Q-curvature in conformal and CR geometries Ambient metric construction of Q-curvature in conformal and CR geometries

2003-03-16

arxiv.org/abs/math/0303184v2

Math. Res. Lett. 10 (2003), no. 5-6, 819--832

Mathematics

Differential Geometry

14 pages, corrected typos and updated references

Scientific paper

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.

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