2022/08/29 by Rafael López, López, Rafael
Computer Science · Mathematics · #49J05 #53A04 #53A10 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2208.13694
openalex publication_date 2022/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.