On Helices and Bertrand Curves in Euclidean 3-Space
Differential Geometry
2014-09-01 v5 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1010.3555,
title = {On Helices and Bertrand Curves in Euclidean 3-Space},
author = {Murat Babaarslan and Yusuf Yayli},
journal= {arXiv preprint arXiv:1010.3555},
year = {2014}
}
Comments
10 pages, 3 figures, Mathematical and Computational Applications (In Press)