标题： 三维中保角测地线的变分性 显示英文标题

标题： Variationality of conformal geodesics in dimension 3

摘要： 共形测地线是在共形流形中一个不变定义的无参数曲线族，它推广了投影联络的无参数测地线/路径。 描述它们的方程是三阶的，并且有一个开放性问题是它们是否由欧拉-拉格朗日方程给出。 在三维空间中（从物理应用的角度来看最简单但也最重要），我们证明无参数共形测地线的方程是变分的。 显示英文摘要

摘要： Conformal geodesics form an invariantly defined family of unparametrized curves in a conformal manifold generalizing unparametrized geodesics/paths of projective connections. The equation describing them is of third order, and it was an open problem whether they are given by an Euler--Lagrange equation. In dimension 3 (the simplest, but most important from the viewpoint of physical applications) we demonstrate that the equation for unparametrized conformal geodesics is variational.