Volume 28, 2022
|Number of page(s)||19|
|Published online||14 February 2022|
Cut time in the sub-Riemannian problem on the Cartan group*
Ailamazyan Program Systems Institute, Russian Academy of Sciences,
2 SISSA, Via Bonomea 265, 34136 Trieste, Italy.
** Corresponding author: email@example.com
Accepted: 24 January 2022
We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Yu. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we obtain a comparison with the known cut times in the sub-Riemannian 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.
Mathematics Subject Classification: 22E25 / 49K15 / 53C17
Key words: Cartan group / sub-Riemannian problem / nilpotent approximation / Carnot groups / Euler elastica / optimal synthesis
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.