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This article is cited in 4 scientific papers (total in 4 papers)
On curves with affine-congruent arcs in an $n$-dimensional affine space
I. V. Polikanova Altai State Pedagogical University, Barnaul, Russian Federation
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
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
Linking options:
https://www.mathnet.ru/eng/smj7649 https://www.mathnet.ru/eng/smj/v63/i1/p180
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Abstract page: | 76 | Full-text PDF : | 21 | References: | 16 | First page: | 8 |
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