Q-prime curvature on CR manifolds

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.

29 pages; minor errors corrected, exposition clarified

Cited by in corpus (15)

• Variation of total Q-prime curvature on CR manifolds
• Chains in CR geometry as geodesics of a Kropina metric
• Nonnegativity of the CR Paneitz operator for embeddable CR manifolds
• Ambient constructions for Sasakian $\eta$-Einstein manifolds
• Extremal metrics for the $Q^{\prime }$-curvature in three dimensions
• Some constructions of formally self-adjoint conformally covariant polydifferential operators
• Analysis of the critical CR GJMS operator
• On the Chern-Moser-Weyl tensor of real hypersurfaces
• CR $Q$-curvature and CR pluriharmonic functions
• Generalizations of the $Q$-prime curvature via renormalized characteristic forms
• Normal form for pseudo-Einstein contact forms and intrinsic CR normal coordinates
• Stability of the existence of a pseudo-Einstein contact form
• An interesting family of conformally invariant one-forms in even dimensions
• Functional Determinant on Pseudo-Einstein 3-manifolds
• On the renormalized volume of tubes over polarized Kähler-Einstein manifolds