Solvable Approximations of 3-dimensional Almost-Riemannian structures

Philippe Jouan (1) , Ronald Manríquez (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 L2S - Laboratoire des signaux et systèmes

In some cases, the nilpotent approximation of an almost-Riemannian structure can degenerate into a constant rank sub-Riemannian one. In those cases, the nilpotent approximation can be replaced by a solvable one that turns out to be a linear ARS on a nilpotent Lie group or a homogeneous space. The distance defined by the solvable approximation is analyzed in the 3Dgeneric cases. It is shown that it is a better approximation of the original distance than the nilpotent one.

Mots clés: Almost-Riemannian geometry; Nilpotent approximation AMS subject classifications: 53C15; 53C17; 22E25; 53B99

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]; Mathématiques [math]

Philippe Jouan, Ronald Manríquez. Solvable Approximations of 3-dimensional Almost-Riemannian structures. Mathematical Control and Related Fields, 2021, ⟨10.3934/mcrf.2021023⟩. ⟨hal-03281505⟩