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

Jaroslav Hrdina; Aleš Návrat; Lenka Zalabová

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

Differential Geometry 2022-08-04 v4 Optimization and Control

Authors: Jaroslav Hrdina , Aleš Návrat , Lenka Zalabová

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

sub-riemannian structure growth vector symmetries geodesics symmetry reduction left-invariant

Cite

@article{arxiv.2102.07428,
  title  = {On symmetries of a sub--Riemannian structure with growth vector $(4,7)$},
  author = {Jaroslav Hrdina and Aleš Návrat and Lenka Zalabová},
  journal= {arXiv preprint arXiv:2102.07428},
  year   = {2022}
}

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

Abstract

Keywords

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