Open AccessSolvable approximations of 3-dimensional almost-Riemannian structures
Author(s) -
Philippe Jouan,
Ronald Manríquez
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021023
Subject(s) - mathematics , nilpotent , rank (graph theory) , homogeneous , space (punctuation) , nilpotent group , pure mathematics , degenerate energy levels , lie group , combinatorics , physics , computer science , quantum mechanics , operating system
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 3D-generic cases. It is shown that it is a better approximation of the original distance than the nilpotent one.