Bendable Surfaces without Visible Deformations of Their Shape
Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 119-130
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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.
@article{MZM_2021_110_1_a10,
author = {I. Kh. Sabitov},
title = {Bendable {Surfaces} without {Visible} {Deformations} of {Their} {Shape}},
journal = {Matemati\v{c}eskie zametki},
pages = {119--130},
year = {2021},
volume = {110},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a10/}
}
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