Arkiv för Matematik

Volume 56 (2018)

Number 2

Fat sub-Riemannian symmetric spaces: the nilpotent case

Pages: 207 – 228

DOI: http://dx.doi.org/10.4310/ARKIV.2018.v56.n2.a1

Authors

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)

Abstract

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

Keywords

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

2010 Mathematics Subject Classification

53C17

Full Text (PDF format)

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