Curves whose pseudo spherical indicatrices are elastic


YÜCESAN A. , Ozkan Tukel G., Tunahan Turhan T. T.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.6, pp.3123-3132, 2018 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1801-44
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.3123-3132

Abstract

The pseudo spherical indicatrix of a curve in Minkowski 3-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter 2-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski 3-space. Then we give some results of solutions of these equations.