Closed geodesics in compact nilmanifolds

We study the density of closed geodesics property on 2-step nilmanifolds Gamma \N, where N is a simply connected 2-step nilpotent Lie group with a left invariant Riemannian metric and Lie algebra N, and Gamma is a lattice in N. We show the density of closed geodesics property holds for quotients of singular, simply connected, 2-step nilpotent Lie groups N which are constructed using irreducible representations of the compact Lie group SU(2).