Cosmological models with flat spatial geometry

The imposition of symmetries or special geometric properties on submanifold s is less restrictive than imposing them on the full spacetime. Starting fr om this idea, in this paper we study irrotational dust cosmological models in which the geometry of the hypersurfaces generated by the fluid velocity is hat, which supposes a relaxation of the restrictions imposed by the cosm ological principle. The method of study combines covariant and tetrad metho ds and exploits the geometrical and physical properties of these models. Th is procedure will allow us to determine all the spacetimes within this clas s as well as to study their properties. Some important consequences and app lications of this study are also discussed.