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2014 A Natural Parameterization of the Roulettes of the Conics Generating the Delaunay Surfaces
Enrique Bendito, Mark J. Bowick, Agustin Medina
J. Geom. Symmetry Phys. 33: 27-45 (2014). DOI: 10.7546/jgsp-33-2014-27-45

Abstract

We derive parametrizations of the Delaunay constant mean curvature surfaces of revolution that follow directly from parametrizations of the conics that generate these surfaces via the corresponding roulette. This uniform treatment exploits the natural geometry of the conic (parabolic, elliptic or hyperbolic) and leads to simple expressions for the mean and Gaussian curvatures of the surfaces as well as the construction of new surfaces.

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Enrique Bendito. Mark J. Bowick. Agustin Medina. "A Natural Parameterization of the Roulettes of the Conics Generating the Delaunay Surfaces." J. Geom. Symmetry Phys. 33 27 - 45, 2014. https://doi.org/10.7546/jgsp-33-2014-27-45

Information

Published: 2014
First available in Project Euclid: 27 May 2017

zbMATH: 1305.53011
MathSciNet: MR3222637
Digital Object Identifier: 10.7546/jgsp-33-2014-27-45

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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