Infinitesimal Bendings of Surfaces with an Edge Under Certain Boundary Conditions

摘要

Infinitesimal bendings of surfaces of positive curvature with a smooth edge are examined. Given on the surface is a continuous field R of simple rays along the edge. To be sought is the existence of infinitesimal surface bendings under which edge points shift by a given value sigma (s) in the direction of R. The necessary and sufficient conditions of solution of the problem, imposed on the function sigma (s), are found. As a corollary of these conditions follow the rigidity of surfaces with sleeve joints of a special form and a strengthening of A.V. Pogorelov's theorem on the rigidity of surfaces when the distances between edge points and some fixed point are stationary. (Author)