Q-prime curvature on CR manifolds

TL;DR

This paper introduces an ambient metric construction of Q-prime curvature on CR manifolds, showing that its integral is a global CR invariant generalizing the Burns-Epstein invariant to higher dimensions.

Contribution

It provides a new ambient metric approach to define Q-prime curvature and proves its integral as a global CR invariant in higher dimensions.

Findings

Integral of Q-prime curvature is a global CR invariant.

Q-prime curvature generalizes the Burns-Epstein invariant.

Construction applies to boundaries of strictly pseudoconvex domains.

Abstract

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.