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Bending of surfaces. III. (English. Russian original) Zbl 1149.53301
J. Math. Sci., New York 149, No. 1, 861-895 (2008); translation from Fundam. Prikl. Mat. 12, No. 1, 3-56 (2006).
Summary: 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).
[For part I,II, cf. I. Ivanova-Karatopraklieva and I. Kh. Sabitov, J. Math. Sci., New York 70, No. 2, 1685–1716 (1994); translation from Itogi Nauki Tekh., Ser. Probl. Geom. 23, 131–184 (1991; Zbl 0835.53003); J. Math. Sci., New York 74, No.3, 997–1043 (1995; Zbl 0861.53002)].

MSC:
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53C24 Rigidity results
53C40 Global submanifolds
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