UKRAINIAN MATHEMATICAL JOURNAL, vol.64, no.8, pp.1277-1289, 2013 (Journal Indexed in SCI)
We study a relaxed elastic line in the general case on an oriented surface. In particular, we obtain a differential equation with three boundary conditions for a generalized relaxed elastic line. Then we analyze the results in a plane, on a sphere, on a cylinder, and on the geodesics of these surfaces.