Catenaries in Riemannian Surfaces
| Autor: | da Silva, Luiz C. B., López, Rafael |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14 pages, 3 figures. Keywords: Catenary, Surface of revolution, Clairaut relation, Grusin plane |
| Databáze: | arXiv |
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