Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\)

DOI10.1134/S0037446616030046zbMath1347.53028OpenAlexW1632332658WikidataQ115248447 ScholiaQ115248447MaRDI QIDQ311240

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 29 September 2016

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446616030046

zbMATH Keywords

Lie algebraLie groupcut locusgeodesicweakly symmetric spaceconjugate setgeodesic orbit spaceinvariant sub-Riemannian metricshortest arc

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Geodesics in global differential geometry (53C22) Differential geometry of symmetric spaces (53C35) Sub-Riemannian geometry (53C17)

Related Items (13)

Sub-Riemannian distance on the Lie group \(\mathrm{SL}(2)\) ⋮ Geodesics and curvatures of special sub-Riemannian metrics on Lie groups ⋮ Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions ⋮ Symmetries in left-invariant optimal control problems ⋮ Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(\operatorname{SU}(1,1)\times \mathbb{R}\) and \(\operatorname{SO}_0(2,1)\times \mathbb{R}\) with three-dimensional generating distributions ⋮ Conjugate time in the sub-Riemannian problem on the Cartan group ⋮ The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane ⋮ Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane ⋮ Geodesics on the group of semi-affine transformations of the Euclidean plane ⋮ Homogeneous sub-Riemannian geodesics on a group of motions of the plane ⋮ Sub-Riemannian distance on the Lie group $\operatorname {SO}_0(2,1)$ ⋮ Homogeneous geodesics in sub-Riemannian geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric
• Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SO}(3)\)
• Homogeneous manifolds with intrinsic metric. II
• A metric characterization of Riemannian submersions
• (Locally) shortest arcs of a special sub-Riemannian metric on the Lie group $\mathrm {SO}_0(2,1)$
• Weakly symmetric Riemannian manifolds with reductive isometry group
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces
• Homogeneous spaces with inner metric and with integrable invariant distributions

This page was built for publication: Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\)