A Curvature Energy Problem on a Timelike Surface


TUKEL G. O. , YÜCESAN A.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.11, no.2, pp.120-125, 2018 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2018
  • Title of Journal : INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Page Numbers: pp.120-125

Abstract

We present a variational study of finding null relaxed elastic lines which are extremals of a geometric energy functional, subject to suitable constraints and boundary conditions on a timelike surface in Minkowski 3-space. We derive an Euler-Lagrange equation for a null relaxed elastic line with regard to geodesic curvature, geodesic torsion and normal curvature of the curve on the timelike surface. Finally, we give some examples for null relaxed elastic lines on the pseudo-sphere and pseudo-cylinder.