(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1993)
The infinitesimal bendings with sliding of higher order of simply connected piecewise (but not globally) convex surfaces _L, obtained by inner pasting together of convex coaxial rotational surfaces, are investigated. The pole of the surfaces is supposed to be smooth point (nonparabolic or parabolic). It is shown that the surfaces _L are nonrigid of any order. Necessary and sufficient conditions are found for extension of a fundamental field of infinitesimal bending with sliding of the 1st order of the surface _L to a field of infinitesimal bending with sliding (allong the parallel L) of the order m>1. Sufficient conditions for rigidity of the surface _L are given.