Diederich-Fornaess and Steinness Indices for Abstract CR Manifolds

Abstract

We propose the concept of Diederich-Fornaess and Steinness indices on compact pseudoconvex CR manifolds of hypersurface type in terms of the D'Angelo 1-form. When the CR manifold bounds a domain in a complex manifold, under certain additional non-degeneracy conditions, those indices are shown to coincide with the original Diederich-Fornaess and Steinness indices of the domain, and CR invariance of the original indices follows.