Lattices and periodic geodesics in pseudoriemannian 2-step nilpotent Lie groups

We give a basic treatment of lattices Gamma in these groups. Certain tori T-F and T-B provide the model fiber and the base for a submersion of Gamma\N. This submersion may not be pseudoriemannian in the usual sense, because the tori may be degenerate. We then begin the study of periodic geodesics in these compact nilmanifolds, obtaining a complete calculation of the period spectrum of certain flat spaces.