On the Oscillations of the Tensor Spin Structure Function

The smallness of the deuteron tensor spin structure function is the necessary condition to extract neutron $g_1$ function neglecting the nuclear effects. The oscillating behavior of the quark tensor spin structure function leading to the zero first moment is shown to be the straightforward consequence of the factorization property and Lorentz covariance. For the singlet contribution the momentum conservation leads to the zero second moment also. The deviations from zero directly measure the gluon contribution.