On symmetries of a sub-Riemannian structure with growth vector (4,7)

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Authors

HRDINA Jaroslav NÁVRAT Aleš ZALABOVÁ Lenka

Year of publication 2023
Type Article in Periodical
Magazine / Source Annali di Matematica Pura ed Applicata
MU Faculty or unit

Faculty of Science

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.
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