  Recently, coherent deeply virtual Compton scattering (DVCS) off $^3$He nuclei
has been proposed to access the neutron generalized parton distributions
(GPDs). In Impulse Approximation (IA) studies, it has been shown, in
particular, that the sum of the two leading twist, quark helicity conserving
GPDs of $^3$He, $H$ and $E$, at low momentum transfer, is dominated by the
neutron contribution, so that $^3$He is very promising for the extraction of
the neutron information. Nevertheless, such an extraction could be not trivial.
A technique, able to take into account the nuclear effects included in the IA
analysis in the extraction procedure, has been therefore developed. In this
work, the IA calculation of the spin dependent GPD $\tilde H$ of $^3$He is
presented for the first time. This quantity is found to be largely dominated,
at low momentum transfer, by the neutron contribution, which could be extracted
using arguments similar to the ones previously proposed for the other GPDs. The
known forward limit of the IA calculation of $\tilde H$, yielding the polarized
parton distributions of $^3$He, is correctly recovered. The knowledge of the
GPDs $H, E$ and $\tilde H$ of $^3$He will allow now the evaluation of the cross
section asymmetries which are relevant for coherent DVCS off $^3$He at
Jefferson Lab kinematics, an important step towards the planning of possible
experiments.
