On Relaxed Elastic Lines of Second Kind on a Curved Hypersurface in the N-Dimensional Euclidean Space

Abstract

In the present paper, the relaxed elastic lines of second kind on an oriented surface in the Euclidean n-space are defined and the Euler-Lagrange equations are derived. Furthermore, an example is presented. Special emphasis is laid on the particular case when these curves are at the same time geodesic. © 2014 Heldermann Verlag.