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 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2018
  • Journal Name: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.120-125
  • Süleyman Demirel University Affiliated: Yes

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.