A new geometrical look at gravity coupled with Yang-Mills fields

A new geometrical framework for tetrad-af ne formulation of gravity, pure or coupled with Yang–Mills elds, is proposed. After analyzing the geometrical prop- erties of the new mathematical setting, eld equations are deduced from a varia- tional principle in the Poincaré–Cartan formalism. A generalized Noether Theorem is stated and classical relationship between symmetries and conserved quantities are recovered in the newer scheme. Some explicit examples are given.