A natural parameterization of the roulettes of the conics generating the Delaunay surfaces

Enrique Bendito; Mark J. Bowick; Agustin Medina

doi:10.7546/jgsp-33-2014-27-45

A natural parameterization of the roulettes of the conics generating the Delaunay surfaces

Enrique Bendito, Mark J. Bowick, Agustin Medina

Department of Physics

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

8 Scopus citations

Abstract

We derive paiamelnzalions of the Delaunay constant mean curvature surfaces of revolution that lollow directly hom parametrrzations ol the conics that generate these surfaces via the coriesponding roulette This uniform treatment ex ploils the natural geomeliy of the conic (parabolic elliptic or hyperbolic) and leads to simple expiessions for the mean and Gaussian cuivatures of the surfaces as well is the construction of new surfaces.

Original language	English (US)
Pages (from-to)	27-45
Number of pages	19
Journal	Journal of Geometry and Symmetry in Physics
Volume	33
DOIs	https://doi.org/10.7546/jgsp-33-2014-27-45
State	Published - Jan 1 2014

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

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abstract = "We derive paiamelnzalions of the Delaunay constant mean curvature surfaces of revolution that lollow directly hom parametrrzations ol the conics that generate these surfaces via the coriesponding roulette This uniform treatment ex ploils the natural geomeliy of the conic (parabolic elliptic or hyperbolic) and leads to simple expiessions for the mean and Gaussian cuivatures of the surfaces as well is the construction of new surfaces.",

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AB - We derive paiamelnzalions of the Delaunay constant mean curvature surfaces of revolution that lollow directly hom parametrrzations ol the conics that generate these surfaces via the coriesponding roulette This uniform treatment ex ploils the natural geomeliy of the conic (parabolic elliptic or hyperbolic) and leads to simple expiessions for the mean and Gaussian cuivatures of the surfaces as well is the construction of new surfaces.

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A natural parameterization of the roulettes of the conics generating the Delaunay surfaces

Abstract

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