2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135173The results of this paper are outdated. Finer versions of them will appear elsewhere.This paper has been withdrawnDifferential GeometryOperator Algebras58J42 (Primary); 53B20, 53A30, 58J40 (Secondary)Noncommutative residue, conformal invariants and lower dimensional volumes in Riemannian geometrytext