Finite and Infinitesimal Flexibility of Semidiscrete Surfaces
Oleg Nikolaevich Karpenkov · Arnold Mathematical Journal · 2015
In this paper we study infinitesimal and finite flexibility for regular semidiscrete surfaces. We prove that regular 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a system of differential equations describing isometric deformations in the case of existence. Further we find a necessary condition of 3-ribbon infinitesimal flexibility. For an arbitrary $$n\ge 3$$ we prove that every regular n-ribbon surface has at most one degree of finite/infinitesimal flexibility. Finally, we discuss the relation between general semidiscrete surface flexibility and 3-ribbon subsurface flexibility. We conclude this paper with one surprising property of isometric deformations of developable semidiscrete surfaces.