Q-prime curvature on CR manifolds

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.

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