Monday, May 27, 2013

1305.5681 (Enrique Bendito et al.)

Delaunay Surfaces    [PDF]

Enrique Bendito, Mark J. Bowick, Agustin Medina
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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