Catenaries in Riemannian surfaces

Luiz C. B. da Silva; Rafael López

doi:10.1007/s40863-023-00399-z

Catenaries in Riemannian surfaces

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

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

201 Downloads (Pure)

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 language	English
Pages (from-to)	389-406
Number of pages	18
Journal	São Paulo Journal of Mathematical Sciences
Volume	18
Early online date	26 Jan 2024
DOIs	https://doi.org/10.1007/s40863-023-00399-z
Publication status	Published - 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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10.1007/s40863-023-00399-zLicence: CC BY

Final Published Version Final published version, 1.61 MBLicence: CC BY

5 Citations
1 Preprint

Catenaries in Riemannian Surfaces
da Silva, L. C. B. & López, R., Jun 2023, arXiv, p. 1-14, 14 p.
Research output: Working paper/Preprint › Preprint

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Cite this

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title = "Catenaries in Riemannian surfaces",

abstract = "The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author (L{\'o}pez, 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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AU - da Silva, Luiz C. B.

AU - López, Rafael

PY - 2024

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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 - catenary

KW - Surface of revolution

KW - Clairaut relation

KW - Grušin plane

KW - α-catenary

U2 - 10.1007/s40863-023-00399-z

DO - 10.1007/s40863-023-00399-z

M3 - Article

SN - 2316-9028

VL - 18

SP - 389

EP - 406

JO - São Paulo Journal of Mathematical Sciences

JF - São Paulo Journal of Mathematical Sciences

ER -

Catenaries in Riemannian surfaces

Abstract

Keywords

ASJC Scopus subject areas

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Catenaries in Riemannian Surfaces

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