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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 1, Pages 167–176
(Mi smj2186)
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This article is cited in 2 scientific papers (total in 2 papers)
An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevskiĭ 3-space
D. A. Slutskiyab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk
Abstract:
We give an example of an infinitesimally nonrigid polyhedron in the Lobachevskiĭ 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron is not stationary under the flex.
Keywords:
infinitesimally nonrigid polyhedron, Lobachevskiĭ space, hyperbolic space, volume, total mean curvature, infinitesimal flex, Schläfli formula.
Received: 28.01.2010
Citation:
D. A. Slutskiy, “An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevskiĭ 3-space”, Sibirsk. Mat. Zh., 52:1 (2011), 167–176; Siberian Math. J., 52:1 (2011), 131–138
Linking options:
https://www.mathnet.ru/eng/smj2186 https://www.mathnet.ru/eng/smj/v52/i1/p167
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Abstract page: | 265 | Full-text PDF : | 68 | References: | 40 |
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