Geodesic
Geometrical equivalence of nilpotent groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 259-270

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In this paper nilpotent torsion free groups are considered. Sufficient conditions are presented when the nilpotent torsion free group is geometrically equivalent to its Mal'tsev completion. Also some results are achieved in the describing of classes of geometrical equivalence of nilpotent class 2 torsion free groups with the small rank of center. 
@article{ZNSL_2006_330_a14,
     author = {A. Tsurkov},
     title = {Geometrical equivalence of nilpotent groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {259--270},
     publisher = {mathdoc},
     volume = {330},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a14/}
}
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A. Tsurkov. Geometrical equivalence of nilpotent groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 259-270. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a14/