Finite and infinitesimal flexibility of semidiscrete surfaces

Karpenkov, Oleg ORCID: 0000-0002-3358-6998 (2015) Finite and infinitesimal flexibility of semidiscrete surfaces. Arnold Mathematical Journal, 1 (04). pp. 403-444.

	Text 1004.2420v3.pdf - Submitted version Download (325kB)
	Text 1004.2420v3.pdf - Submitted version Download (325kB)

Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	Semidiscrete surfaces, Flexibility, Infinitesimal flexibility
Subjects:	?? QA ??
Depositing User:	Symplectic Admin
Date Deposited:	18 Dec 2015 10:47
Last Modified:	19 Jan 2023 07:38
DOI:	10.1007/s40598-015-0025-3
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2043380

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