Corresponding to these derivations, we give two formulas for the Q-curvature in §2. In either case, our key observation is the following transformation law of log t, where t is a conformal scale (a fiber coordinate of the bundle G determined by a section g ∈ [g]):

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Q-prime curvature, which was introduced by J. Case and P. Yang, is a local invariant of pseudo-hermitian structure on CR manifolds that can be defined only when the Q-curvature vanishes identically. It is considered as a secondary invariant on CR manifolds and, in 3-dimensions, its integral agrees with the Burns-Epstein invariant, a Chern-Simons type invariant in CR geometry. We give an ambient metric construction of the Q-prime curvature and study its basic properties. In particular, we show that, for the boundary of a strictly pseudoconvex domain in a Stein manifold, the integral of the Q-prime curvature is a global CR invariant, which generalizes the Burns-Epstein invariant to higher dimensions.Comment: 29 pages; minor errors corrected, exposition clarifie

We show that on conformal manifolds of even dimension n ≥ 4 there is no conformally invariant natural differential operator between density bundles with leading part a power of the Laplacian ∆ k for k > n/2. This shows that a large class of invariant operators on conformally flat manifolds do not generalise to arbitrarily curved manifolds and that the theorem of Graham, Jenne, Mason and Sparling, asserting the existence of curved version of ∆ k for 1 ≤ k ≤ n/2, is sharp.

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