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Remarks to Sabitov’s hypothesis on the stationarity of volume in the case of an infinitesimal bending of a surface. (Russian) Zbl 0687.53007

Connelly stated the following conjecture: Every banded polyhedron does not change its volume in the process of the bending. Sabitov suggested to consider this conjecture in the case when the bending is an infinitesimal one. His conjecture is: The volume of a closed surface does not change in the process of an infinitesimal bending. In this paper the author shows that Sabitov’s conjecture is not true for polyhedra, but it is true for the surfaces of revolution with a regular meridian which does not contain segments, orthogonal to the rotation axis.
Reviewer: S.Hineva

MSC:

53A05 Surfaces in Euclidean and related spaces
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