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 Mat. Sb., 2014, Volume 205, Number 12, Pages 111–140 (Mi msb8343)

Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles

I. Kh. Sabitov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study infinitesimal bendings of surfaces of revolution with flattening at the poles. We begin by considering the minimal possible smoothness class $C^1$ both for surfaces and for deformation fields. Conditions are formulated for a given harmonic of a first-order infinitesimal bending to be extendable into a second order infinitesimal bending. We finish by stating a criterion for nonrigidity of second order for closed surfaces of revolution in the analytic class. We also give the first concrete example of such a nonrigid surface.
Bibliography: 15 entries.

Keywords: surfaces of revolution, pole, order of flattening, second-order infinitesimal bendings, rigidity.

 Funding Agency Grant Number Russian Foundation for Basic Research 12-01-90415-ÓÊÐà

DOI: https://doi.org/10.4213/sm8343

Full text: PDF file (674 kB)
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English version:
Sbornik: Mathematics, 2014, 205:12, 1787–1814

Bibliographic databases:

UDC: 514.772.35
MSC: 53A05

Citation: I. Kh. Sabitov, “Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles”, Mat. Sb., 205:12 (2014), 111–140; Sb. Math., 205:12 (2014), 1787–1814

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8343
• https://doi.org/10.4213/sm8343
• http://mi.mathnet.ru/eng/msb/v205/i12/p111

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175
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