Infinitesimal first- and second-order deformations of ribbed surfaces of revolution,preserving the normal curvature or geodesic torsion of the boundary parallel

Infinitesimal deformations of ribbed surfaces of revolution S_n with preservation of the normal curvature (A) or geodesic torsion (B) of the boundary parallel are investigated. The following are proved: a convex surface S_n is rigid under deformations (A) and (B); there are nonconvex surfaces S_n that are nonrigid under deformations (A) and (B); any surface S_n has second-order rigidity under deformations (A); a surface S_n that is nonrigid under these deformations.Translated from Mateniaticheskie Zametki, Vol. 10, No. 2, pp. 135–144, August, 1971.