Catenaries in Riemannian Surfaces

Luiz C. B. da Silva, Rafael López

Research output: Working paper/PreprintPreprint

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Abstract

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.
Original languageEnglish
PublisherarXiv
Pages1-14
Number of pages14
DOIs
Publication statusPublished - Jun 2023

Keywords

  • Catenary
  • Surface of revolution
  • Clairaut relation
  • Grusin plane

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