Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

DOI10.1134/S0012266115110087zbMath1350.53045OpenAlexW2259370670WikidataQ115251408 ScholiaQ115251408MaRDI QIDQ258185

Alexey P. Mashtakov, Yuri L. Sachkov

Publication date: 17 March 2016

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266115110087

zbMATH Keywords

Pontryagin maximum principleLiouville integrableSR geodesicSR-shortest curve

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General properties and structure of real Lie groups (22E15) Sub-Riemannian geometry (53C17)

Related Items (6)

On sub-Riemannian geodesics in \(\mathrm{SE}(3)\) whose spatial projections do not have cusps ⋮ On integrability of certain rank 2 sub-Riemannian structures ⋮ Tracking of lines in spherical images via sub-Riemannian geodesics in \(\mathrm{SO}(3)\) ⋮ Asymptotics of Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space ⋮ Left-Invariant Sub-Riemannian Engel Structures: Abnormal Geodesics and Integrability ⋮ A note about integrable systems on low-dimensional Lie groups and Lie algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion
• Sub-Riemannian structures on 3D Lie groups
• Extremal trajectories and Maxwell strata in sub-Riemannian problem on group of motions of pseudo-Euclidean plane
• Sub-Riemannian geodesics on the three-dimensional solvable non-nilpotent Lie group \(\mathrm{SOLV}^-\)
• Control theory on Lie groups
• A nonintegrable sub-Riemannian geodesic flow on a Carnot group
• Integrability of left-invariant sub-Riemannian structures on the special linear group \(\mathrm{SL}_2(\mathbb R)\)
• Conjugate points in nilpotent sub-Riemannian problem on the Engel group
• Superintegrable Hamiltonian systems: Geometry and perturbations
• On 2-Step, Corank 2, Nilpotent Sub-Riemannian Metrics
• Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
• Integrable Hamiltonian systems on complex Lie groups

This page was built for publication: Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups