Carnot group

In mathematics, a Carnot group is a simply connected nilpotent Lie group, together with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra. Carnot groups have a Carnot–Carathéodory metric. They were introduced by Parnu (1982, 1989) and Mitchell (1985).

References

• Mitchell, John (1985), "On Carnot-Carathéodory metrics", Journal of Differential Geometry 21 (1): 35–45, ISSN 0022-040X, MR806700, http://projecteuclid.org/getRecord?id=euclid.jdg/1214439462 
• Pansu, Pierre (1982), Géometrie du groupe d'Heisenberg, Thesis, Universite Paris VII, http://www.math.u-psud.fr/~pansu/pansu_These_1982.html 
• Pansu, Pierre (1989), "Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un", Annals of Mathematics. Second Series 129 (1): 1–60, doi:10.2307/1971484, ISSN 0003-486X, MR979599