Geodesic
Systoles on Heisenberg groups with Carnot--Carath\'eodory metrics
Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 347-374

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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. 
@article{SM_2001_192_3_a1,
     author = {V. V. Dontsov},
     title = {Systoles on {Heisenberg} groups with {Carnot--Carath\'eodory} metrics},
     journal = {Sbornik. Mathematics},
     pages = {347--374},
     publisher = {mathdoc},
     volume = {192},
     number = {3},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_3_a1/}
}
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V. V. Dontsov. Systoles on Heisenberg groups with Carnot--Carath\'eodory metrics. Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 347-374. http://geodesic.mathdoc.fr/item/SM_2001_192_3_a1/