Relaxed elastic line in a Riemannian manifold


Ozkan G., YÜCESAN A.

TURKISH JOURNAL OF MATHEMATICS, vol.38, no.4, pp.746-752, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 4
  • Publication Date: 2014
  • Doi Number: 10.3906/mat-1303-38
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.746-752

Abstract

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.