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"
}