Sub-Riemannian problem on three dimensional solvable Lie group
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Abstract
In this article we consider sub-Riemannian problem on three dimensional solvable Lie group. This is based on a construction of Hamiltonian structure for the geodesic flow of Carnot-Caratheodory metrics via the Pontryagin maximum principle.References
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[2] Е.П. Аксенов, Специальные функции в небесной механике, - M: Наука, 1986. -321 с.
[3] U.Boscain, F.Rossi, Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and lens spaces, - Preprint SISSA, 2007. - 24 p.
[4] O.Calin, D.-Ch.Chang, I.Markina, SubRiemannian geometry on the sphere S3.//arxiv.org>math>arXiv:0804.1695, - 2008. - 13 p.
[5] И.С.Градштейн, И.М.Рыжик, Таблицы интегралов, сумм, рядов и произведений, - М.: Физматгиз, 1963. - 1100 с.
[6] I.A.Taimanov, Integrable geodesic flows of non-holonomic metrics. // J.Dynam. Control Sistem 3(1997), - 129-147 p.
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How to Cite
Mazhitova, A. D. (2010). Sub-Riemannian problem on three dimensional solvable Lie group. Journal of Mathematics, Mechanics and Computer Science, 65(2), 11–18. Retrieved from https://bm.kaznu.kz/index.php/kaznu/article/view/228
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Geometry
