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arXiv · 2306.04013

Catenaries in Riemannian Surfaces

Luiz C. B. da Silva·Rafael López
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Abstract

The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author [L\'opez, 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 Gru\v{s}in plane.

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Luiz C. B. da Silva, Rafael López. 2023-06-06. Catenaries in Riemannian Surfaces. https://arxiv.org/abs/2306.04013

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