2010/04/14 by Karpenkov, Oleg · 1 citation
#52C25 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1004.2420
In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 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≥ 3 we prove that every generic 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.