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 [Formula: see text]. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves on [Formula: see text]. As a result, we classify these critical curves as elastic magnetic curves of the Darboux vector family.

中文翻译：

---

表面铁磁和超顺磁模型的弹性磁曲线

我们有兴趣定义新的能量泛函并使用变分方法和 Darboux 方程求解它们。也就是说，我们的目标是在规则曲面上定义一类新的弹性曲线[公式：见正文]。我们进一步改进了一种替代方法，以找到作用于[公式：见正文]上的一类磁曲线的弯曲能量泛函的临界点。因此，我们将这些临界曲线归类为 Darboux 矢量族的弹性磁曲线。