On Relaxed Elastic Lines of the Second Type on an Oriented Surface in the Galilean Space G3

Abstract

In the present paper, the relaxed elastic line of the second type on an oriented surface in the Galilean space G<inf>3</inf> 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. © 2017, Springer International Publishing.