Relaxed elastic line in a Riemannian manifold

Authors : Gözde Özkan, Ahmet Yücesan

Pages : 746-752

Doi:10.3906/mat-1303-38

View : 15 | Download : 12

Publication Date : 9999-12-31

Article Type : Makaleler

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 k, 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.
Keywords : Relaxed elastic line, Riemannian manifold, geodesic curvature, space forms