  In this paper we discuss a class of models that address the issue of
explaining the gravitational dynamics at the galactic scale starting from a
geometric point of view. Instead of claiming the existence of some hidden
coupling between dark matter and baryons, or abandoning the existence of dark
matter itself, we consider the possibility that dark matter and gravity have
some non trivial interaction able to modify the dynamics at astrophysical
scales. This interaction is implemented assuming that dark matter gets
non--minimally coupled with gravity at suitably small scales and late times.
After showing the predictions of the model in the Newtonian limit we also
discuss the possible origin of it non-minimal coupling. This investigation
seems to suggest that phenomenological mechanisms envisaged for the dark matter
dynamics, such as the Bose--Einstein condensation of dark matter halos, could
be connected to this class of models.
