On Darboux rotation axis of lightlike curves


Sekerci G., ÇÖKEN A. C. , Ekici C.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, vol.13, no.9, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 9
  • Publication Date: 2016
  • Doi Number: 10.1142/s0219887816501127
  • Journal Name: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: Lightlike curve, Frenet trihedron, Darboux vector, Lorentzian space

Abstract

In this paper, by used Frenet trihedron for a lightlike curve, the motion of Darboux rotation axis is seperated to two simultaneous rotation motions. These rotation motions are that tangent and normal vectors of lightlike curve rotate around each other. But, the angular speeds of them are different. Then, by doing the similar operations, we obtain that Darboux axis rotates around spacelike vector of Frenet trihedron of the lightlike curve and this spacelike vector rotates around Darboux axis. Consequently, we obtain the series of Darboux vectors by this way. So, simple mechanisms can be formed.