The relation betweenk-th order rigidity and analytic nondeformability of surfaces

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 (k2) 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Theses and Reports of the All-Union Conference on Geometry in the Large, Novosibirsk (1987)] the proof of which, still unpublished, is based on another idea. Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 98–104, 1991.