2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36278A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is obtained by using a new parametrization of arbitrary cotetrads to define a set of configurational variables to be used in the ADM metric action. Seven of the fourteen first class constraints have the form of the vanishing of canonical momenta. A comparison is made with other models of tetrad gravity and with the ADM canonical formalism for metric gravity. The phase space expression of various 4-tensors is explicitly given.68 pages, revtex, revised version with additionsGeneral Relativity and Quantum Cosmologytext