  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.
