Geodesic
Nilmanifolds with Carnot--Carath\'eodory metrics
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 64-75

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We describe systolic constants for some important examples of metric spaces with inner metric. 
@article{ZNSL_2000_266_a5,
     author = {V. V. Dontsov},
     title = {Nilmanifolds with {Carnot--Carath\'eodory} metrics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--75},
     publisher = {mathdoc},
     volume = {266},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a5/}
}
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V. V. Dontsov. Nilmanifolds with Carnot--Carath\'eodory metrics. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 64-75. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a5/