On Helices and Bertrand Curves in Euclidean 3-Space

Mathematical and Computational Applications

Babaarslan, Murat¹ 

关键词: Helix;    Bertr;    curve;    Sabban frame;    Spherical images;   

DOI  :  10.3390/mca18010001

学科分类：计算数学

来源: mdpi

【 摘 要 】

In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix, we demonstrate that the curve corresponding to the spherical image of its the principal normal indicatrix is both a Bertrand curve and a circular helix.

【 授权许可】

CC BY