标题： 欧拉在洛伦兹-闵可夫斯基平面上的问题扩展 显示英文标题

标题： Extension of a problem of Euler in Lorentz-Minkowski plane

摘要： 在本文中，我们研究洛伦兹-闵可夫斯基空间$\mathbb{L}^2$中的曲线，这些曲线是相对于原点的惯性矩的临界点。 这扩展了欧拉在洛伦兹情形下提出的一个问题。 我们得到了$\mathbb{L}^2$中静止曲线的显式解，并区分曲线是类空的还是类时的。 我们还提供了一种方法，通过关于光锥的对称性和反演，将静止的类空曲线转换为静止的类时曲线，反之亦然。 最后，我们解决了在所有连接两个与原点共线的点的类空曲线中最大化能量的问题。 显示英文摘要

摘要： In this paper we study curves in Lorentz-Minkowski space $\mathbb{L}^2$ that are critical points of the moment of inertia with respect to the origin. This extends a problem posed by Euler in the Lorentzian setting. We obtain explicit solutions for stationary curves in $\mathbb{L}^2$ distinguishing if the curve is spacelike or timelike. We also give a method to carry stationary spacelike curves into stationary timelike curves and vice versa via symmetries and inversions about the lightlike cone. Finally, we solve the problem of maximizing the energy among all spacelike curves joining two given points which are collinear with the origin.