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 $S^2_\lambda$ 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 $S_\lambda^2(S_\lambda^1,S_\lambda^0)$