Renormalized characteristic forms of the Cheng--Yau metric and global CR invariants

Abstract

For each invariant polynomial $\Phi$, we construct a global CR invariant via the renormalized characteristic form of the Cheng--Yau metric on a strictly pseudoconvex domain. When the degree of $\Phi$ is 0, the invariant agrees with the total $Q^{\prime }$-curvature. When the degree is equal to the CR dimension, we construct a primed pseudo-hermitian invariant ${\mathcal{I}}_{\Phi }^{\prime }$ which integrates to the corresponding CR invariant. These are generalizations of the ${\mathcal{I}}^{\prime }$-curvature on CR five-manifolds, introduced by Case--Gover.

39 pages, final version