Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1303-38
Keywords
Relaxed elastic line, Riemannian manifold, geodesic curvature, space forms
First Page
746
Last Page
752
Recommended Citation
ÖZKAN, GÖZDE and YÜCESAN, AHMET
(2014)
"Relaxed elastic line in a Riemannian manifold,"
Turkish Journal of Mathematics: Vol. 38:
No.
4, Article 11.
https://doi.org/10.3906/mat-1303-38
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss4/11
