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

@article{Fefferman2003AmbientMC, title={Ambient metric construction of Q-curvature in conformal and CR geometries}, author={Charles Fefferman and Kengo Hirachi}, journal={Mathematical Research Letters}, year={2003}, volume={10}, pages={819-831} }

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… Expand

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