This article is cited in 2 papers

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevskiĭ 3-space

D. A. Slutskiy<sup>ab

a</sup> 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.

UDC: 514.113.5+514.132

Received: 28.01.2010

 English version: Siberian Mathematical Journal, 2011, 52:1, 131–138

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