Relaxed elastic line in a Riemannian manifold
TURKISH JOURNAL OF MATHEMATICS, cilt.38, sa.4, ss.746-752, 2014 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 4
- Basım Tarihi: 2014
- Doi Numarası: 10.3906/mat-1303-38
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.746-752
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
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.