On symmetries of a sub-Riemannian structure with growth vector (4,7)
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Annali di Matematica Pura ed Applicata |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s10231-022-01242-6 |
| Doi | http://dx.doi.org/10.1007/s10231-022-01242-6 |
| Keywords | Nilpotent algebras; Lie symmetry group; Carnot groups; Sub-Riemannian geodesics |
| Description | We study symmetries of specific left-invariant sub-Riemannian structure with filtration (4, 7) and their impact on sub-Riemannian geodesics of corresponding control problem. We show that there are two very different types of geodesics, they either do not intersect the fixed point set of symmetries or are contained in this set for all times. We use the symmetry reduction to study properties of geodesics. |
| Related projects: |