Catenaries in Riemannian surfaces

Luiz C. B. da Silva (Lead / Corresponding author), Rafael López

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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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
Number of pages18
JournalSão Paulo Journal of Mathematical Sciences
Early online date26 Jan 2024
DOIs
Publication statusE-pub ahead of print - 26 Jan 2024

Keywords

  • Catenary
  • catenary
  • Surface of revolution
  • Clairaut relation
  • Grušin plane
  • α-catenary

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • General Mathematics

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