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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 1, Pages 180–196
DOI: https://doi.org/10.33048/smzh.2022.63.112 (Mi smj7649) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On curves with affine-congruent arcs in an $n$-dimensional affine space

I. V. Polikanova

Altai State Pedagogical University, Barnaul, Russian Federation
Full-text PDF (326 kB) Citations (3)
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DOI: https://doi.org/10.33048/smzh.2022.63.112
Abstract: Considering an $n$-dimensional affine space, we demonstrate that enics (moment curves) are the only nondegenerate curves in the class of $C^n$-smooth curves every two oriented arcs of which are affine congruent. The proof is reduced to a system of functional-differential equations.
Keywords: curves with affine congruent arcs, straight line, parabola, cubic, enic, moment curve, Veronese curve, system of functional equations.
Received: 23.07.2020
Revised: 13.01.2021
Accepted: 11.10.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 1, Pages 149–162
DOI: https://doi.org/10.1134/S0037446622010128
Bibliographic databases:
Document Type: Article
UDC: 514.754.24
Language: Russian
Citation: I. V. Polikanova, “On curves with affine-congruent arcs in an $n$-dimensional affine space”, Sibirsk. Mat. Zh., 63:1 (2022), 180–196; Siberian Math. J., 63:1 (2022), 149–162
Citation in format AMSBIB
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\by I.~V.~Polikanova
\paper On~curves with affine-congruent~arcs in an~$n$-dimensional affine space
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 1
\pages 180--196
\mathnet{http://mi.mathnet.ru/smj7649}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4440273}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 1
\pages 149--162
\crossref{https://doi.org/10.1134/S0037446622010128}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124011927}
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    • This publication is cited in the following 3 articles:
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