标题： 黎曼曲面上的悬链线 显示英文标题

标题： Catenaries in Riemannian Surfaces

摘要： 悬链线的概念最近由第二作者扩展到了球面和双曲平面[López, arXiv:2208.13694]。 在本工作中，我们定义了任何黎曼面上的悬链线。 曲面上的悬链线是势能泛函的临界点，其中势能是通过到固定参考测地线的内在距离来计算的。 采用参考测地线周围的半测地坐标，我们利用曲率来表征悬链线。 最后，在重新审视空间形式的悬链线后，我们考虑了旋转曲面（建立了克莱罗关系）、直纹面和格鲁辛平面。 显示英文摘要

摘要： The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author [L\'opez, arXiv:2208.13694]. In this work, we define catenaries on any Riemannian surface. A catenary on a surface is a critical point of the potential functional, where we calculate the potential with the intrinsic distance to a fixed reference geodesic. Adopting semi-geodesic coordinates around the reference geodesic, we characterize catenaries using their curvature. Finally, after revisiting the space-form catenaries, we consider surfaces of revolution (where a Clairaut relation is established), ruled surfaces, and the Gru\v{s}in plane.