Generalizations of the Q-prime curvature via renormalized characteristic forms

Abstract

The Q-prime curvature is a local pseudo-Einstein invariant on CR manifolds defined by Case and Yang, and Hirachi. Its integral, the total Q-prime curvature, gives a non-trivial global CR invariant. On the other hand, Marugame has constructed a family of global CR invariants via renormalized characteristic forms, which contains the total Q-prime curvature. In this paper, we introduce a generalization of the Q-prime curvature for each renormalized characteristic form, and show that its integral coincides with Marugame's CR invariant. We also study generalizations of the critical CR GJMS operator and the P-prime operator, which are related to the transformation laws of our new curvatures under conformal change.