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Geometry and Applications
March 13-16, 2000
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University
Novosibirsk, Russia

Organizers
Yu.G. Rushetnyak (Chair of Program Committee; Russia), V.V. Vershinin (Chair of Organizing Committee; Russia), A.A. Borisenko (Ukraine), Yu.D. Burago (Russia), V.M. Gol'dshtein (Israel), M.L. Gromov (France), I.G. Nikolaev (USA/Russia), S.P. Novikov (USA/Russia), A.V. Pogorelov (Ukraine), I.Kh. Sabitov (Russia)

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Necessary conditions for a framework to be flexible
by
Victor Alexandrov
Sobolev Institute of Mathematics, Novosibirsk, Russia

It is well-known that if a framework (or polyhedron) is either first order rigid or second-order rigid then it is rigid, i.e. one can not change continuously its spatial shape without changing lengths of bars (or of edges, respectively). On the other hand, R.Connelly and H.Servatius constructed a flexible framework which is third-order rigid [1].

We are going to present some necessary conditions for a framework to be flexible, i.e. to be non rigid. Our main result can be formulated as follows. Let F be a framework which admits only one linearly independent nontrivial first-order flex and let there exists an integer N such that F is Nth-order rigid. Then F is rigid.

Reference: [1] R.Connelly, H.Servatius. Higher-order rigidity - what is the proper definition? Discrete Comput. Geom. 11, No.2, 193-200 (1994).

Date received: February 21, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadw-34.