The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane
Identificadores
URI: https://hdl.handle.net/10481/92712Metadatos
Afficher la notice complèteAuteur
López Camino, RafaelEditorial
Springer Nature
Director
López, RafaelMateria
Hanging chain problem Sphere Hyperbolic plane Catenary Rotational surface Prescribed curvature
Date
2024-06-19Referencia bibliográfica
López, R. The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane. J Nonlinear Sci 34, 75 (2024). https://doi.org/10.1007/s00332-024-10056-0
Patrocinador
Universidad de Granada; MCIN/AEI/10.13039/501100011033 PID2020-117868GB-I00Résumé
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.