2018/06/06 by Şahin, Tevfik
#49Q20 #53A35 #53A55 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1806.03980
In this paper, we consider the classical variational problem in the Galilean space. we develop the Euler-Lagrange equations for a elastic line on an oriented surface in the Galilean 3-dimensional space G3. Using the varia- tion method, we will try to give some characterization for the solution curve (the elastic line) of energy equation described by the total squared curvature function of a curve on an oriented surface in G3. Finally, we will investigate whether or not the relaxed elastic curves are on a geodesic.