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.
Relaxed elastic line, Riemannian manifold, geodesic curvature, space forms
ÖZKAN, GÖZDE and YÜCESAN, AHMET
"Relaxed elastic line in a Riemannian manifold,"
Turkish Journal of Mathematics: Vol. 38:
4, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss4/11