General Nilpotent and Solvable Approximations of Almost-Riemannian Structures

Yacine Chitour (1) , Philippe Jouan (2) , Ronald Manríquez (1)

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

It is first shown that the nilpotent or the solvable approximation of an almost-Riemannian structure at a singular point is always a linear almost-Riemannian structure on a Lie group or a homogeneous space. The generic properties of almost-Riemannian structures are then investigated in all dimensions and the generic nilpotent and solvable approximations are identified.

Mots clés: Almost-Riemannian geometry; Nilpotent approximation; Solvable approximation; Genericity

Domaines: Optimisation et contrôle [math.OC]

Yacine Chitour, Philippe Jouan, Ronald Manríquez. General Nilpotent and Solvable Approximations of Almost-Riemannian Structures. 2022. ⟨hal-03636478v2⟩