Construction of vectorial moments via direction curves

Abstract

<abstract><p>In a recent paper Tunçer ^{[<xref ref-type="bibr" rid="b14">14</xref>]} described and examined the moment vectors (T -dual, N-dual, B-dual curve) of the curve with respect to the origin of the vector by using T(s), N(s), B(s) and the position vector of the curve. With the inspiration this paper provided, we define some new associated curves called dual-direction curves as integral curves of a vector field in this study. They are generated with the help of vectorial moments of a space curve in three-dimensional Euclidean space. We attain some connections between the Frenet apparatus of dual-direction curves and main curves. With the help of these dual-direction curves, certain ways to construct helices are determined. Finally, we exemplify these curves with their figures.</p></abstract>