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

Charles Fefferman·Kengo Hirachi
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Abstract

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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Charles Fefferman, Kengo Hirachi. 2003-03-16. Ambient metric construction of Q-curvature in conformal and CR geometries. https://doi.org/10.4310/mrl.2003.v10.n6.a9

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