Publication detail
On symmetries of a sub-Riemannian structure with growth vector (4,7)
HRDINA, J. NÁVRAT, A. ZALABOVÁ, L.
English title
On symmetries of a sub-Riemannian structure with growth vector (4,7)
Type
journal article in Web of Science
Language
en
Original abstract
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.
English abstract
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.
Keywords in English
Nilpotent algebras; Lie symmetry group; Carnot groups; Sub-Riemannian geodesics
Released
17.07.2022
Publisher
SPRINGER HEIDELBERG
Location
HEIDELBERG
ISSN
0003-4622
Volume
1
Number
1
Pages from–to
1–14
Pages count
14
BIBTEX
@article{BUT178837,
author="Jaroslav {Hrdina} and Aleš {Návrat} and Lenka {Zalabová},
title="On symmetries of a sub-Riemannian structure with growth vector (4,7)",
year="2022",
volume="1",
number="1",
month="July",
pages="1--14",
publisher="SPRINGER HEIDELBERG",
address="HEIDELBERG",
issn="0003-4622"
}