2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107643We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective structures and construct a Casimir operator depending on a projective Cartan connection. We attach a scalar parameter to every space of differential operators, and prove the existence of a quantization except when this parameter belongs to a discrete set of resonant values.27 pages, 5 figuresDifferential Geometry58A05, 53B05, 46L65, 58J70text