Cut locus of a left invariant Riemannian metric on \(\mathrm{SO}_3\) in the axisymmetric case

DOI10.1016/j.geomphys.2016.09.005zbMath1352.53044arXiv1504.05472OpenAlexW1562689769WikidataQ115353026 ScholiaQ115353026MaRDI QIDQ335855

A. V. Podobryaev, Yuri L. Sachkov

Publication date: 2 November 2016

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05472

zbMATH Keywords

Riemannian geometrygeodesicscut locussub-Riemannian geometrycut time\(\mathrm{SO}_3\)

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20) Sub-Riemannian geometry (53C17)

Related Items (10)

Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions ⋮ Diameter of the Berger sphere ⋮ Unnamed Item ⋮ Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie groups ⋮ Symmetries in left-invariant optimal control problems ⋮ Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems ⋮ On the subRiemannian cut locus in a model of free two-step Carnot group ⋮ Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane ⋮ Antipodal Points and Diameter of a Sphere ⋮ Homogeneous geodesics in sub-Riemannian geometry

Cites Work

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• Sub-Riemannian structures on 3D Lie groups
• Maxwell strata in the Euler elastic problem
• Cut loci of Berger's spheres
• Control theory from the geometric viewpoint.
• The conjugate locus for the Euler top I. The axisymmetric case
• Complete description of the Maxwell strata in the generalized Dido problem
• Invariant Carnot–Caratheodory Metrics on $S^3$, $SO(3)$, $SL(2)$, and Lens Spaces

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