On Relaxed Elastic Lines of the Second Type on an Oriented Surface in the Galilean Space G(3)
RESULTS IN MATHEMATICS, vol.71, no.3-4, pp.955-982, 2017 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 71 Issue: 3-4
- Publication Date: 2017
- Doi Number: 10.1007/s00025-017-0663-y
- Journal Name: RESULTS IN MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.955-982
- Keywords: Elastic curve, Galilean space, Geodesics, Euler-Lagrange equations
- Ondokuz Mayıs University Affiliated: Yes
Abstract
In the present paper, the relaxed elastic line of the second type on an oriented surface in the Galilean space G(3) is defined. For the relaxed elastic lines of the second type which are lying on a given oriented surface the Euler-Lagrange equations are derived. In particular, we investigate whether they can be geodesic or curvature lines. In the last section we present some examples to confirm our claim.