On the scalar and dual formulations of the curvature theory of line trajectories in the Lorentzian space


Ayyildiz N. , Yuecesan A.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.43, no.6, pp.1339-1355, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 6
  • Publication Date: 2006
  • Doi Number: 10.4134/jkms.2006.43.6.1339
  • Title of Journal : JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1339-1355

Abstract

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.