Narrow Results

We are interested in defining new energy functionals and solving them by using the variational approach method and Darboux equations. That is, we aim to define a new class of elastic curves on the regular surface $\mathrm{\Lambda }$. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves on $\mathrm{\Lambda }$. As a result, we classify these critical curves as elastic magnetic curves of the Darboux vector family.