2 papers
math.DG2020
Bicycle paths, elasticae and sub-Riemannian geometry
Andrey Ardentov, Gil Bor, Enrico Le Donne +2
We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose f…
math.DG2018
Sub-Finsler geodesics on the Cartan group
A. Ardentov, E. Le Donne, Yu. Sachkov
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler norm. We start by giving a detailed presentation of the…