Geodesic
Bendable Surfaces without Visible Deformations of Their Shape
Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 119-130.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the slide bendings of cylindrical and conical surfaces are trivial only in the cases of a right circular cylinder and a right circular cone, and that in all other cases, such bendings are nontrivial, although the surfaces do not change as loci in $\mathbb{R}^3$.
Keywords: curve, initial point of measuring length, slide bending, cylindrical surface, conical surface, trivial and nontrivial slide bendings of cylindrical and conical surfaces. 
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I. Kh. Sabitov. Bendable Surfaces without Visible Deformations of Their Shape. Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 119-130. http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a10/

[1] V. F. Kagan, Osnovy teorii poverkhnostei v tenzornom izlozhnii, Chast vtoraya, OGIZ, M.-L., 1948 | MR

[2] M. Spivak, A comprehensive introduction to Differential Geometry, Vol. 5, Publish or Perish, Wilmington, DE, 1979 | MR

[3] I. Kh. Sabitov, “Kvazikonformnye otobrazheniya poverkhnosti, porozhdennye ee izometricheskimi preobrazovaniyami, i izgibaniya poverkhnosti na sebya”, Fundament. i prikl. matem., 1:1 (1995), 281–288 | MR | Zbl