  The equations for gravitational plane waves produced by a typical binary
system as a solution of linear approximation of Einstein equations is derived.
The dynamics of the corresponding gravitational field is analyzed in a
4-dimensional space-time manifold, endowed with a metric and taking into
account the torsion. In this context, the geometrical reason of the existence
of torsion due to the presence of gravitational waves, as an asymmetry of
connection coefficients with respect of the swapping of indices's is
highlighted. In a laser interferometer gravitational detector The delay time
between the arrivals of the two laser beams traveling back and forth along the
two arms of in presence of gravitational waves, is interpreted from this point
of view. The geometrical interpretation of torsion, links this delay time to
the breaking of the parallelogram formed by the trajectories of the laser beams
in space-time. This delay is calculated for a typical NS-NS binary pulsar in
two specific orientations with respect of the experimental device,
corresponding to different polarizations of the gravitational waves. These
values are related to the relative length variation of the detector's arms in
presence of gravitational waves, and shown to be completely equivalent to the
results obtained in the context of the standard General Relativity.
