  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 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.
