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(Locally) shortest arcs of a special sub-Riemannian metric on the Lie group $ \mathrm{SO}_0(2,1)$


Author: V. N. Berestovskiĭ
Translated by: the author
Original publication: Algebra i Analiz, tom 27 (2015), nomer 1.
Journal: St. Petersburg Math. J. 27 (2016), 1-14
MSC (2010): Primary 22E30, 49J15, 53C17
DOI: https://doi.org/10.1090/spmj/1373
Published electronically: December 7, 2015
MathSciNet review: 3443263
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Abstract | References | Similar Articles | Additional Information

Abstract: The geodesics, shortest arcs, cut loci, and conjugate sets are found for a left-invariant sub-Riemannian metric on the Lie group $ \mathrm {SO}_0(2,1)$ under the condition that the metric is right-invariant relative to the Lie subgroup $ \mathrm {SO}(2)\subset \mathrm {SO}_0(2,1)$.


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Additional Information

V. N. Berestovskiĭ
Affiliation: Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences
Email: vberestov@inbox.ru

DOI: https://doi.org/10.1090/spmj/1373
Keywords: Geodesic, Lie algebra, Lie group, left-invariant sub-Riemannian metric, shortest arc.
Received by editor(s): June 10, 2014
Published electronically: December 7, 2015
Additional Notes: Partially supported by RFBR (grant no. 14-01-00068-p) and by a grant of the Government of the Russian Federation for the State Support of Scientific Research (agreement no. 14.B25.31.0029)
Article copyright: © Copyright 2015 American Mathematical Society