2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107562In this paper we give a survey of the constructions in math.DG/0510061 of several new invariants for CR and contact manifolds. The latter extend previous constructions of Hirachi and Boutet de Monvel. In addition, we give simple algebro-geometric arguments proving that Hirachi's invariant vanishes on strictly pseudoconvex CR manifolds of dimension 4m+1.To appear in proceedings of the workshop "Analytic geometry of the Bergman kernel and related topics", RIMS, Kyoto University, Japan, Dec. 12-16, 2005Differential GeometryComplex VariablesPrimary 32A25; Secondary 32V20, 53D35, 58J40, 58J42text