Solvable Approximations of 3-dimensional Almost-Riemannian structures

International audienceIn 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