Turkish Journal of Mathematics
DOI
10.3906/mat-1303-38
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.
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
