Timelike quaternion frame of a non-lightlike curve

ÖZDEMİR M., ERGİN A. A.

Beitrage zur Algebra und Geometrie, vol.49, no.2, pp.325-333, 2008 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2008
  • Journal Name: Beitrage zur Algebra und Geometrie
  • Journal Indexes: Scopus
  • Page Numbers: pp.325-333
  • Keywords: Frenet formulas, Non-lightlike curves, Split quaternion
  • Akdeniz University Affiliated: Yes

Abstract

A rotation matrix can be generated by a unit timelike quaternion in the three dimensional Minkowski space. In this paper, we correspond columns of this rotation matrix to Frenet vectors of a nonlightlike curve and we find a reformulation of Frenet's formulas of nonlightlike curves in terms of the timelike quaternions in the Minkowski 3-space. Moreover, we do same things for the parallel transport frame. MSC 2000: 53B30, 53A04, 15A66. © 2008 Heldermann Verlag.