Catenaries in Riemannian surfaces
Metadatos
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Springer Nature
Materia
Catenary α-catenary Surface of revolution
Fecha
2024-01-26Referencia bibliográfica
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
Patrocinador
Morá Miriam Rozen Gerber fellowship for Brazilian postdocs; Faculty of Physics Postdoctoral Excellence Fellowship; IMAG; Research Group “Problemas variacionales en geometría”, Junta de Andalucía (FQM 325); MINECO/MICINN/FEDER grant no. PID2020-117868GB-I00; “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCINN/AEI/10.13039/501100011033/CEX2020-001105-MResumen
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.