RESUMEN
Fibre bundle formulations of field theory are
considered approximately by the appropiate vector bundle. The fibre
verbiein (frame) is considered as depended indirectly on an element f of the fibre group, which we choose as a harmonic mapping from the
base manifold. We do the same for the other fundamental geometrical quantity called the connection, but choose another independent
harmonic mapping h instead of f. Aditionally, we generalize the torsion-free condition to this more general
vector bundle other than target bundle, by using the pullback mapping. A new gauge invariant Lagragian is propossed.