Title: Cut time in sub-Riemannian problem on Engel group
Authors: A.A. Ardentov, Yu.L. Sachkov
Journal title: ESAIM: COCV
The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic rank two sub-Riemannian problems on four-dimensional manifolds.
The global optimality of extremal trajectories is studied via geometric control theory. The global diffeomorphic structure of the exponential mapping is described. As a consequence, the cut time is proved to be equal to the first Maxwell time corresponding to discrete symmetries of the exponential mapping.
ArXiv ID (ENG): 1408.6651