On Curves with Affine-Congruent Arcs in an -Dimensional Affine Space

Considering an  -dimensional affine space, we demonstrate that enics (moment curves) are the only nondegenerate curves in the class of -smooth curves every two oriented arcs of which are affine congruent. The proof is reduced to a system of functional-differential equations.

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Bibliographic Details
Published in:Siberian mathematical journal 2022, Vol.63 (1), p.149-162
Main Author: Polikanova, I. V.
Format: Article
Language:English
Subjects:
Differential equations
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Description
Summary:Considering an  -dimensional affine space, we demonstrate that enics (moment curves) are the only nondegenerate curves in the class of -smooth curves every two oriented arcs of which are affine congruent. The proof is reduced to a system of functional-differential equations.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446622010128