The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane López Camino, Rafael López, Rafael Hanging chain problem Sphere Hyperbolic plane Catenary Rotational surface Prescribed curvature Funding for open access publishing: Universidad de Granada/CBUA. This work has been partially supported by the Project PID2020-117868GB-I00 and MCIN/AEI/10.13039/501100011033. 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. 2024-06-19T11:53:16Z 2024-06-19T11:53:16Z 2024-06-19 journal article 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 https://hdl.handle.net/10481/92712 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Springer Nature