@misc{10481/91555,
year = {2024},
month = {1},
url = {https://hdl.handle.net/10481/91555},
abstract = {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.},
organization = {Morá Miriam
Rozen Gerber fellowship for Brazilian postdocs},
organization = {Faculty of Physics Postdoctoral Excellence Fellowship},
organization = {IMAG},
organization = {Research Group “Problemas variacionales en geometría”, Junta de Andalucía (FQM 325)},
organization = {MINECO/MICINN/FEDER grant no. PID2020-117868GB-I00},
organization = {“María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCINN/AEI/10.13039/501100011033/CEX2020-001105-M},
publisher = {Springer Nature},
keywords = {Catenary},
keywords = {α-catenary},
keywords = {Surface of revolution},
title = {Catenaries in Riemannian surfaces},
doi = {10.1007/s40863-023-00399-z},
author = {Barbosa da Silva, Luiz Carlos and López Camino, Rafael},
}