On helices and Bertrand curves in Euclidean 3-space

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BABAARSLAN M., YAYLI Y.

Mathematical and Computational Applications, vol.18, no.1, pp.1-11, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.3390/mca18010001
  • Journal Name: Mathematical and Computational Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1-11
  • Keywords: Bertrand curve, Helix, Sabban frame, Spherical images
  • Ankara University Affiliated: Yes

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.