论文标题
球体和双曲机中的悬挂链问题
The hanging chain problem in the sphere and in the hyperbolic plane
论文作者
论文摘要
在本文中，引入了球体和双曲机中链链曲线的概念。在这两个空间中，当链轴的势能取决于悬挂链的形状时，链轴的形状是由与给定的空间大地测量的距离确定的。链状的几种特征是根据曲线的曲率和其单位正常在环境空间的矢量场中所产生的角度的。此外，在双曲机平面中，我们扩展了链式链球链球骨的概念，将参考地测量替换为肌关系或双曲线距离。
In this paper, the notion of the catenary curve in the sphere and in the hyperbolic plane is introduced. In both spaces, a catenary is defined as the shape of a hanging chain when its potential energy is determined by the distance to a given geodesic of the space. Several characterizations of the catenary are established in terms of the curvature of the curve and of the angle that its unit normal makes with a vector field of the ambient space. Furthermore, in the hyperbolic plane, we extend the concept of catenary substituting the reference geodesic by a horocycle or the hyperbolic distance by the horocycle distance.
