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Dupin Cyclides

Ottens, L.J.C. (2012) Dupin Cyclides. Bachelor's Thesis, Mathematics.

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Abstract

A Dupin cyclide is the envelope of a one-parameter family of spheres tangent to three fixed spheres. By studying the relation between a Dupin cyclide and a torus of revolution, partly from an inversive geometry approach, we prove that the definition of the first is equivalent to being the conformal image of a torus of revolution. Here we define a torus of revolution such that all standard tori fall within the definition. Furthermore, we look into the curvature lines of a Dupin cyclide, where we use amongst others the theorems of Joachimsthal and Meusnier, and prove that the two previous characterizations of a Dupin cyclide are equivalent with being a surface all whose lines of curvature are circles.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:47
Last Modified: 15 Feb 2018 07:47
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/9941

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