Geodesic
Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles
Sbornik. Mathematics, Tome 205 (2014) no. 12, pp. 1787-1814

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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, order of flattening, second-order infinitesimal bendings, rigidity.
Mots-clés : pole 
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     author = {I. Kh. Sabitov},
     title = {Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles},
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I. Kh. Sabitov. Second-order infinitesimal bendings of surfaces of revolution with flattening at the poles. Sbornik. Mathematics, Tome 205 (2014) no. 12, pp. 1787-1814. http://geodesic.mathdoc.fr/item/SM_2014_205_12_a6/