TY - UNPB
T1 - Catenaries in Riemannian Surfaces
AU - da Silva, Luiz C. B.
AU - López, Rafael
PY - 2023/6
Y1 - 2023/6
N2 - 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.
AB - 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.
KW - Catenary
KW - Surface of revolution
KW - Clairaut relation
KW - Grusin plane
U2 - 10.48550/arXiv.2306.04013
DO - 10.48550/arXiv.2306.04013
M3 - Preprint
SP - 1
EP - 14
BT - Catenaries in Riemannian Surfaces
PB - arXiv
ER -