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

We give a basic treatment of lattices $Γ$ in these groups. Certain tori $T_F$ and $T_B$ provide the model fiber and the base for a submersion of $Γ\backslash N$. 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.

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