Catenaries in Riemannian Surfaces

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 -