  The imposition of symmetries or special geometric properties on submanifolds
is less restrictive than to impose them in the full space-time. Starting from
this idea, in this paper we study irrotational dust cosmological models in
which the geometry of the hypersurfaces generated by the fluid velocity is
flat, which supposes a relaxation of the restrictions imposed by the
Cosmological Principle. The method of study combines covariant and tetrad
methods that exploits the geometrical and physical properties of these models.
This procedure will allow us to determine all the space-times within this class
as well as to study their properties. Some important consequences and
applications of this study are also discussed.
