Abstract
It is proved that a surface of class C 3 admitting only one linearly independent, infinitely small, first order bending and having rigidity of order k (k≥2) is analytically nondeformable. This result can also be obtained from Sabitov's more general result [Theses and Reports of the All-Union Conference on Geometry in the Large, Novosibirsk (1987)] the proof of which, still unpublished, is based on another idea.
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References
N. V. Efimov, "Qualitative problems of the theory of bendings of surfaces," Uspekhi Mat. Nauk,3, No. 2/24, 45–158 (1948).
N. V. Efimov, "Some propositions on rigidity and nondeformability," Uspekhi Mat. Nauk,7, No. 5/51, 215–224 (1948).
I. Kh. Sabitov, "Some results and problems of local theory of bendings," Theses of the All-Union Conference on Geometry in the Large [in Russian], Inst. Mat. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk (1987), p. 108.
Additional information
Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 98–104, 1991.
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Perlova, N.G. The relation betweenk-th order rigidity and analytic nondeformability of surfaces. J Math Sci 69, 900–904 (1994). https://doi.org/10.1007/BF01250821
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DOI: https://doi.org/10.1007/BF01250821