  Variational formalism in the extended phase space for fields is applied to
gravity. It is shown that the requirement of invariance under arbitrary local
inertial frames implies a coupling of torsion to a 3-form of matter fields on
the one hand and to a 3-form (related to the Einstein tensor) on the other.
Gravitational dynamics is restricted to torsion zero surface in the extended
phase space for Einstein-Hilbert action.
