Systoles on Heisenberg groups with Carnot–Carathéodory metrics

The systolic properties of the nilmanifolds $\mathscr N^{2n+1}$ associated with the higher Heisenberg groups $H_{2n+1}$ are studied. Effective estimates of the systolic constants $\sigma(\mathscr N^{2n+1})$ in the Carnot–Carathéodory geometry, as functions of the parameters defining a uniform lattice on $H_{2n+1}$, are obtained.