Abstract
The authors find geodesics, shortest arcs, a diameter, a cut locus, and conjugate sets for a left-invariant sub-Riemannian metric on the Lie group SO(3) under the condition that the metric is right-invariant relative to the Lie subgroup SO(2) ⊂ SO(3).
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Original Russian Text Copyright © 2015 Berestovskiĭ V.N. and Zubareva I.A.
The first author was partially supported by the Russian Foundation for Basic Research (Grant 14–01–00068–a) and a grant of the Government of the Russian Federation for the State Support of Scientific Research (Agreement No. 14.B25.31.0029).
Novosibirsk; Omsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 4, pp. 762–774, July–August, 2015; DOI: 10.17377/smzh.2015.56.404.
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Berestovskiĭ, V.N., Zubareva, I.A. Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group SO(3). Sib Math J 56, 601–611 (2015). https://doi.org/10.1134/S0037446615040047
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DOI: https://doi.org/10.1134/S0037446615040047