Abstract
It is proved that an analytic surface does not admit a nontrivial analytic infinitesimal deformation of the second order satisfying one of the following conditions: a) preservation of the normal curvature of a planar closed convex curve belonging to the surface; b) each point of a closed curve belonging to the surface slides in a rectifiable curve.
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E. Rembs, “Verbiegungen höherer Ordnung und ebene Flächenrinnen,” Math. Zeitschr.,36, 110–121 (1932).
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Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 233–242, August, 1973.
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Perlova, N.G. On some second-order rigidity conditions for analytic surfaces. Mathematical Notes of the Academy of Sciences of the USSR 14, 692–697 (1973). https://doi.org/10.1007/BF01147116
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DOI: https://doi.org/10.1007/BF01147116