Cut time in the subRiemannian problem on the Cartan group
Abstract
We study the subRiemannian structure determined by a leftinvariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachkov for the subRiemannian Cartan problem. Along the proof, we obtain a comparison with the known cut times in the subRiemannian Engel group, and a sufficient (generic) condition for the uniqueness of the length minimizer between two points. Hence we reduce the optimal synthesis to solving a certain system of equations in elliptic functions.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.06730
 Bibcode:
 2021arXiv210706730A
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  Differential Geometry;
 22E25;
 49K15;
 53C17
 EPrint:
 23 pages, 3 figures