INTEGRAL CHARACTERIZATIONS FOR TIMELIKE AND SPACELIKE CURVES ON THE LORENTZIAN SPHERE S-1(3)


Kazaz M., Ugurlu H. H. , Ozdemir A.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, vol.32, pp.25-31, 2008 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 32
  • Publication Date: 2008
  • Title of Journal : IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Page Numbers: pp.25-31

Abstract

V. Dannon showed that spherical curves in E-4 can be given by Frenet-like equations, and he then gave an integral characterization for spherical curves in E-4. In this paper, Lorentzian spherical timelike and spacelike curves in the space time are shown to be given by Frenet-like equations of timelike and spacelike curves in the Euclidean space E-3 and the Minkowski 3-space R-1(3). Thus, finding an integral characterization for a Lorentzian spherical R-1(4)-timelike and spacelike curve is identical to finding it for E-3 curves and R-1(3)-timelike and spacelike curves. In the case of E-3 curves, the integral characterization coincides with Dannon's.