RIGIDITY OF TOROID FORMED BY REVOLUTION OF PARALLELOGRAM

Abstract

One of the main tasks of the deformation theory is to point out to the rigid and flexible surfaces. In this paper we signify a torus like class of surfaces generated by parallelogram in E3. It is proved that this class is rigid due to infinitesimal bending. Infinitesimal bending of generated surfaces is considered using Cohn-Vossen’s method.