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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 4, Pages 731–748
(Mi smj1422)
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This article is cited in 20 scientific papers (total in 20 papers)
Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups
V. N. Berestovskii, I. A. Zubareva Omsk State University
Abstract:
The exact shapes of spheres are found for some nonholonomic left-invariant metrics on three-dimensional Lie groups: the Heisenberg group $H$, $SO(3)$, and $SL_2\mathbb R$. By easy geometric arguments, the task is reduced to solving isoperimetric problems for planes of constant Gaussian curvature.
Received: 20.01.2000
Citation:
V. N. Berestovskii, I. A. Zubareva, “Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups”, Sibirsk. Mat. Zh., 42:4 (2001), 731–748; Siberian Math. J., 42:4 (2001), 613–628
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https://www.mathnet.ru/eng/smj1422 https://www.mathnet.ru/eng/smj/v42/i4/p731
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Abstract page: | 427 | Full-text PDF : | 132 |
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