Diederich-Fornaess and Steinness indices for abstract CR manifolds

Abstract: We propose the concept of Diederich--Forn{\ae}ss 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 condition, those indices are shown to coincide with the original Diederich--Forn{\ae}ss and Steinness indices of the domain, and CR invariance of the original indices follows.