2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/207089We study the Husain-Kuchar model by introducing a new action principle similar to the self-dual action used in the Ashtekar variables approach to Quantum Gravity. This new action has several interesting features; among them, the presence of a scalar time variable that allows the definition of geometric observables without adding new degrees of freedom, the appearance of a natural non-degenerate four-metric and the possibility of coupling ordinary matter.LaTeX, 22 pages, accepted for publication in Phys. Rev. DGeneral Relativity and Quantum Cosmologytext