  In several nearby intermediate luminosity early-type galaxies, recent
observations at large radii have shown a indications of a lack of dark matter,
substantially at odds with the prediction from the CDM hierarchical merger
models. Here we discuss a pilot observational project for the study of the
internal kinematical and dynamical properties of this remarkable sample of
galaxies. Using the VIMOS-IFU in its high spectral resolution mode, it would be
possible to investigate the regions up to about 1.2 effective radii, taking
advantage of the much larger field of view and telescope diameter. This will
allow to disclose the presence of any kinematical substructures which could
affect the conclusion on the mass modeling and definitely clarify the inner
structure of this particular class of early-type galaxies.
