The concept of centre of mass of two particles in 2D spaces of constant Gaussian curvature is discussed by recalling the notion of "relativistic rule of lever" introduced by Galperin [6] (Comm. Math. Phys. 154 (1993), 63–84), and comparing it with two other definitions of centre of mass that arise naturally on the treatment of the 2-body problem in spaces of constant curvature: firstly as the collision point of particles that are initially at rest, and secondly as the centre of rotation of steady rotation solutions. It is shown that if the particles have distinct masses then these definitions are equivalent only if the curvature vanishes and instead lead to three different notions of centre of mass in the general case.

中文翻译：

---

关于恒曲率空间中两个粒子的质心的一些评论

通过回想起Galperin提出的“杠杆相对论法则”的概念，讨论了在恒定高斯曲率的2D空间中两个粒子的质心概念。6（通讯数学物理学。 154（1993），63-84），并将其与在2体问题的治疗在恒定曲率的空间中自然产生的质心的其他两个定义进行比较：首先作为最初是静止的，其次是稳定旋转解的旋转中心的粒子的碰撞点。结果表明，如果粒子具有不同的质量，则这些定义仅在曲率消失且在一般情况下导致三个不同的质心概念时才是等效的。