Publication result detail

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

HRDINA, J.; NÁVRAT, A.; ZALABOVÁ, L.

Original Title

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

English Title

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

Type

WoS Article

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

Nilpotent algebras; Lie symmetry group; Carnot groups; Sub-Riemannian geodesics

Key words in English

Nilpotent algebras; Lie symmetry group; Carnot groups; Sub-Riemannian geodesics

Authors

HRDINA, J.; NÁVRAT, A.; ZALABOVÁ, L.

RIV year

2023

Released

17.07.2022

Publisher

SPRINGER HEIDELBERG

Location

HEIDELBERG

ISBN

0003-4622

Periodical

ANNALI DI MATEMATICA PURA ED APPLICATA

Volume

1

Number

1

State

Republic of Italy

Pages from

1

Pages to

14

Pages count

14

URL

https://link.springer.com/article/10.1007/s10231-022-01242-6

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)",
  journal="ANNALI DI MATEMATICA PURA ED APPLICATA",
  year="2022",
  volume="1",
  number="1",
  pages="1--14",
  doi="10.1007/s10231-022-01242-6",
  issn="0003-4622",
  url="https://link.springer.com/article/10.1007/s10231-022-01242-6"
}