Abstract
We find the distances between arbitrary elements of the Lie group SL(2) for the left invariant sub-Riemannian metric also invariant with respect to the right shifts by elements of the Lie subgroup SO(2) ⊂ SL(2), in other words, the invariant sub-Riemannian metric on the weakly symmetric space (SL(2) × SO(2))/ SO(2) of Selberg.
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Novosibirsk; Omsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 1, pp. 22–35, January–February, 2017; DOI: 10.17377/smzh.2017.58.103.
The authors were supported in part by the Russian Foundation for Basic Research (Grant 14–01–00068–a) and the Government of the Russian Federation for the State Support of Scientific Research (Agreement 14.B25.31.0029).
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Berestovskiĭ, V.N., Zubareva, I.A. Sub-Riemannian distance on the Lie group SL(2). Sib Math J 58, 16–27 (2017). https://doi.org/10.1134/S0037446617010037
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DOI: https://doi.org/10.1134/S0037446617010037