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

N. G. Perlova

Rostov State University

Abstract: 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.

UDC: 513.73

Received: 16.06.1970

 English version: Mathematical Notes, 1971, 10:2, 506–511

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