Relaxed elastic line in a Riemannian manifold


Ozkan G. , YÜCESAN A.

TURKISH JOURNAL OF MATHEMATICS, cilt.38, ss.746-752, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 38 Konu: 4
  • Basım Tarihi: 2014
  • Doi Numarası: 10.3906/mat-1303-38
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.746-752

Özet

We obtain a differential equation with 2 boundary conditions for a relaxed elastic line in a Riemannian manifold. This differential equation, which is found with respect to constant sectional curvature G, geodesic curvature kappa, and 2 boundary conditions, gives a more direct and more geometric approach to questions concerning a relaxed elastic line in a Riemannian manifold. We give various theorems and results in terms of a relaxed elastic line. Consequently, we examine the concept of a relaxed elastic line in 2- and 3-dimensional space forms.