Geodesic
Bending of surfaces.~III
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 1, pp. 3-56

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A survey of works on discrete and continuous rigidity/nonrigidity and infinitesimal rigidity/nonrigidity of multidimensional surfaces, mainly in Euclidean spaces, is given. As a starting point for the methods of investigation, one considers three forms of the main theorem of the theory of surfaces (in local coordinates, in the invariant form, and in terms of exterior differential forms). 
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I. Ivanova-Karatopraklieva; P. E. Markov; I. Kh. Sabitov. Bending of surfaces.~III. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 1, pp. 3-56. http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a0/