Arkiv för Matematik

Volume 56 (2018)

Number 2

Fat sub-Riemannian symmetric spaces: the nilpotent case

Pages: 207 – 228



D. M. Almeida (Faculdade de Matemática, Universidade Federal de Uberlandia, Brazil)

E. Falbel (Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris, France; and Ouragan-INRIA, Paris, France)


In this paper we start the classification of strongly bracket-generated sub-symmetric spaces. We prove a structure theorem and analyze the nilpotent case.


sub-Riemannian geometry, sub-symmetric space, fat distribution, two-step nilpotent Lie algebra

2010 Mathematics Subject Classification


This paper was written while the first author was a CAPES Posdoctoral fellow (Grant 6124/12-7) at Institut de Mathématiques d’Université Pierre et Marie Curie, Paris VI. She thanks L’équipe d’Analyse Complexe et Géométrie for their kind hospitality. The second author was supported in part by the ANR through the project Structure Géométriques et Triangulations.

Received 27 February 2016

Received revised 24 October 2017

Accepted 3 November 2017

Published 24 May 2022