Sub-Riemannian manifolds and nilpotent Lie groups

Alessandro Ottazzi
UNSW

Abstract

The motion planning problem consists of finding curves that connect two given points in a geodesic metric space. Algorithms exist to construct such curves in the setting of nilpotent Lie groups endowed with sub-Riemannian metrics. We consider the question of when sub-Riemannian manifolds are equivalent to sub-Riemannian nilpotent Lie groups, in the sense that solutions to the motion planning problem can be transferred between them. We illustrate this with some examples. The results are the outcome of various collaborations.