@misc{10481/92712,
year = {2024},
month = {6},
url = {https://hdl.handle.net/10481/92712},
abstract = {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.},
organization = {Universidad de Granada},
organization = {MCIN/AEI/10.13039/501100011033  PID2020-117868GB-I00},
publisher = {Springer Nature},
keywords = {Hanging chain problem},
keywords = {Sphere},
keywords = {Hyperbolic plane},
keywords = {Catenary},
keywords = {Rotational surface},
keywords = {Prescribed curvature},
title = {The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane},
author = {López Camino, Rafael},
}