  We examine the moduli space of oriented locally homogeneous manifolds of Type
A which have non-degenerate symmetric Ricci tensor both in the setting of
manifolds with torsion and also in the torsion free setting where the dimension
is at least 3. These exhibit phenomena that is very different than in the case
of surfaces. In dimension 3, we determine all the possible symmetry groups in
the torsion free setting.
