Journal for Geometry and Graphics 18 (2014), No. 1, 081--095
Copyright Heldermann Verlag 2014
On Relaxed Elastic Lines of Second Kind on a Curved Hypersurface in the n-Dimensional 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. 8-10/104, 1040 Vienna, Austria
stachel@dmg.tuwien.ac.at
We define the relaxed elastic lines of second kind on an oriented surface in the Euclidean n-space and derive the Euler-Lagrange 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, Euler-Lagrange equation.
MSC: 53A07; 49Q20, 53C22
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