Catenaries in Riemannian surfaces Barbosa da Silva, Luiz Carlos López Camino, Rafael Catenary α-catenary Surface of revolution The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author (López, arXiv: 2208. 13694). In this work, we define catenaries on any Riemannian surface. A catenary on a surface is a critical point of the potential functional, where we calculate the potential with the intrinsic distance to a fixed reference geodesic. Adopting semi-geodesic coordinates around the reference geodesic, we characterize catenaries using their curvature. Finally, after revisiting the space-form catenaries, we consider surfaces of revolution (where a Clairaut relation is established), ruled surfaces, and the Grušin plane. 2024-05-09T06:55:04Z 2024-05-09T06:55:04Z 2024-01-26 journal article da Silva, L.C.B., López, R. Catenaries in Riemannian surfaces. São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-023-00399-z https://hdl.handle.net/10481/91555 10.1007/s40863-023-00399-z eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature