Infinitesimal bendings of some classes of rotational surfaces with mixed curvature

Abstract

The infinitesimal bendings of first order of three families of rotational surfaces $S_{\lambda }^2$, $S_{\lambda }^1$ and $S_{\lambda }^0$ ($\lambda$ is a parameter), with a mixed Gaussian curvature are investigated. The surface $S_{\lambda }^2$ are doubly connected, $S_{\lambda }^1$-simly connected, $S_{\lambda }^0$ - closed, and they haven't any inner asymptotic parallels. The boudary of the surfaces consists of asymptotic parallels and their poles are smooth-nonparabolic or parabolic, or conic points. It is proved that a countable set of nonrigid surfaces exists in $S_{\lambda }^2(S_{\lambda }^1,S_{\lambda }^0)$