Abstract

Anisotropic Delaunay surfaces are surfaces of revolution that have constant anisotropic mean curvature. We show how the generating curves of such surfaces can be obtained as the trace of a point held in a fixed position relative to a curve that is rolled without slipping along a line. This generalizes the Delaunay’s classical construction for surfaces of revolution with constant mean curvature. Our result is given as a corollary of a new geometric description of the rolling curve of a general plane curve. Also, we characterize anisotropic Delaunay curves by using their isothermic self-duality.

Keywords

roulette, rolling curve, anisotropic, Delaunay surface

Mathematical Subject Classification

Primary: 58E12

Secondary: 49Q10

Authors