Delaunay Surfaces

Constant mean curvature cylinders in euclidean 3-space

The Delaunay surfaces, being surfaces of revolution, are the simplest constant mean curvature cylinders [1]. Delaunay surfaces lie in associate families of twizzlers, which have screw-motion symmetry.
A Delaunay unduloid, and cutaway view of a Delaunay nodoid.
A twizzler, in the associate family of a Delaunay surface.
The associate family of a Delaunay surface.
A flow through the one-parameter family of Delaunay unduloids and nodoids.


  1. C Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, J. Math. Pures et Appl. Sér. 1 6 (1841), 309–320.