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

By Charles Fefferman, K. Hirachi. 2003

159 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3d1a4ab1efc9492b806c5f6dcb0cb54dce1e9538

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

CR invariant powers of the sub-Laplacian (2003, unknown): “D G ] 9 J an 2”
Juhl's formulae for GJMS operators and Q-curvatures (2012, background): “oving the factor of n/2 − N. The critical case may also be deduced without this argument of analytic continuation in the dimension by using the realization (−1) n/2Q n = −∆e (logt)|ρ=0,t=1 derived in [FH]. Namely, write ∆en/2(logt)| ρ=0,t=1 = ∆en/2−1 v w∆(loge t) |ρ=0,t=1. Direct calculation gives w”
What is Q-Curvature? (2008, unknown): “The following construction of Q is due to Fefferman and Hirachi [7].”
An extension problem for the CR fractional Laplacian (2013, background): “It is a conformal invariant in the sense that, for a change of contact form θ̂ = e2wθ, eQ = Q + Pmw, as it was shown in [23].”
CR-Tractors and the Fefferman Space (2006, methodology): “In [17], via the Fefferman metric, a CR Q-curvature was defined and studied, while in [24] the Fefferman metric was used as one of the two main construction techniques for the CR invariant powers of the sub-Laplacian.”