Extremals of a left-invariant sub-Finsler metric on the Engel group

DOI10.1134/S0037446620040023zbMath1455.53087arXiv2001.01503OpenAlexW3046006830MaRDI QIDQ2203436

I. A. Zubareva, Valeriĭ Nikolaevich Berestovskiĭ

Publication date: 7 October 2020

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

Full work available at URL: https://arxiv.org/abs/2001.01503

zbMATH Keywords

geodesicEngel groupextremalleft-invariant sub-Finsler metric

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Sub-Riemannian geometry (53C17) Hamilton-Jacobi equations (35F21)

Related Items (2)

Horizontal joinability in canonical 3-step Carnot groups with corank 2 horizontal distributions ⋮ Geodesic fields for Pontryagin type C⁰-Finsler manifolds

Cites Work

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• Sub-Finsler geometry in dimension three
• Geometry of sub-Finsler Engel manifolds
• Maxwell strata and cut locus in the sub-Riemannian problem on the Engel group
• Generalized solutions with the first-order derivatives in \(L_ p\) to the flow problem for the Stokes system
• Sub-Finsler structures on the Engel group
• Conjugate points in nilpotent sub-Riemannian problem on the Engel group
• Geodesics in the Heisenberg group: an elementary approach
• Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group
• Cut time in sub-riemannian problem on engel group
• Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups
• Convex trigonometry with applications to sub-Finsler geometry
• The Isoperimetric Problem in the Minkowski Plane

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