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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2021 Volume 110, Issue 1, Pages 119–130 (Mi mzm13037)

Bendable Surfaces without Visible Deformations of Their Shape

I. Kh. Sabitov

Lomonosov Moscow State University

Abstract: 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.

UDC: 513

Received: 09.02.2021
Revised: 28.02.2021

DOI: 10.4213/mzm13037


 English version:
Mathematical Notes, 2021, 110:1, 126–134

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© Steklov Math. Inst. of RAS, 2024