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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$\Gamma\backslash N$. This submersion may not be pseudoriemannian in the usualsense, because the tori may be degenerate. We then begin the study of periodicgeodesics in these compact nilmanifolds, obtaining a complete calculation ofthe period spectrum of certain flat spaces.

Lattices and Periodic Geodesics in Pseudoriemannian 2-step Nilpotent Lie Groups