Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups

zbMath1481.53042arXiv1906.05511MaRDI QIDQ4965831

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 10 March 2021

Full work available at URL: https://arxiv.org/abs/1906.05511

zbMATH Keywords

optimal controlLie algebraLie groupnormal geodesicmathematical pendulum(co)adjoint representationleft-invariant (sub-)Finsler metricleft-invariant (sub-)Riemannian metric

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Sub-Riemannian geometry (53C17)

Related Items (5)

Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups with three-dimensional generating distributions ⋮ Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(SU(2)\times{ \mathbb{R} }\) and \(SO(3)\times{ \mathbb{R} }\) with three-dimensional generating distributions ⋮ 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 ⋮ Extremals of a left-invariant sub-Finsler metric on the Engel group ⋮ Abnormal extremals of left-invariant sub-Finsler quasimetrics on four-dimensional Lie groups

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