
Journal for Geometry and Graphics 18 (2014), No. 1, 081095 Copyright Heldermann Verlag 2014 On Relaxed Elastic Lines of Second Kind on a Curved Hypersurface in the nDimensional Euclidean Space Ayhan Sarioglugil Dept. of Mathematics, Science and Arts Faculty, Ondokuz Mayis University, 55139 Samsun, Turkey ayhans@omu.edu.tr Ayhan Tutar Dept. of Mathematics, Science and Arts Faculty, Ondokuz Mayis University, 55139 Samsun, Turkey atutar@omu.edu.tr Hellmuth Stachel Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstr. 810/104, 1040 Vienna, Austria stachel@dmg.tuwien.ac.at We define the relaxed elastic lines of second kind on an oriented surface in the Euclidean nspace and derive the EulerLagrange equations. Furthermore, an example is presented. Special emphasis is laid on the particular case when these curves are at the same time geodesic. Keywords: Relaxed elastic line, geodesic curves, intrinsic equation, EulerLagrange equation. MSC: 53A07; 49Q20, 53C22 [ Fulltextpdf (323 KB)] for subscribers only. 