Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric

DOI10.1134/S0037446614050012zbMath1311.53033WikidataQ115248494 ScholiaQ115248494MaRDI QIDQ486358

Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 15 January 2015

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

zbMATH Keywords

Lie algebraLie groupHamiltonian systemPontryagin maximum principletime-optimal problemcontrol functioninvariant sub-Riemannian metricshortest arcnormal geodesic

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Sub-Riemannian geometry (53C17)

Related Items (12)

Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups ⋮ Geodesics and shortest arcs of a special sub-Riemannian metric 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 ⋮ Equality of the capacity and module of a condenser on a sub-Finsler space ⋮ Locally isometric coverings of the Lie group $ \mathrm{SO}_0(2,1)$ with special sub-Riemannian metric ⋮ Sub-Riemannian distance in the Lie groups SU(2) and SO(3) ⋮ Curvatures of homogeneous sub-Riemannian manifolds ⋮ The geodesics of a sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane ⋮ (Locally) shortest arcs of a special sub-Riemannian metric on the Lie group $\mathrm {SO}_0(2,1)$ ⋮ Geodesics on the group of semi-affine transformations of the Euclidean plane ⋮ Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SO}(3)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles
• Sub-Riemannian geometry
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Homogeneous manifolds with intrinsic metric. I
• Homogeneous manifolds with intrinsic metric. II
• Generalized solutions with the first-order derivatives in \(L_ p\) to the flow problem for the Stokes system
• Geodesics of a left-invariant nonholonomic Riemannian metric on the group of motions of the Euclidean plane
• Geodesics in the Heisenberg group: an elementary approach
• Abnormal Minimizers
• Shortest paths for sub-Riemannian metrics on rank-two distributions

This page was built for publication: Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric