Fat sub-Riemannian symmetric spaces: the nilpotent case

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

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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