Rolling construction for anisotropic Delaunay surfaces

Koiso Miyuki, Bennett Palmer
2008 Pacific Journal of Mathematics  
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
more » ... ane curve. Also, we characterize anisotropic Delaunay curves by using their isothermic self-duality. MSC2000: primary 58E12; secondary 49Q10.
doi:10.2140/pjm.2008.234.345 fatcat:sfei3zpt2re53kdu3kjcb5d5bi