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.