Constant mean curvature surfaces via integrable dynamical system
dg-ga
2009-10-28 v1 Differential Geometry
Abstract
It is shown that the equation which describes constant mean curvature surface via the generalized Weierstrass-Enneper inducing has Hamiltonian form. Its simplest finite-dimensional reduction has two degrees of freedom, integrable and its trajectories correspond to well-known Delaunay and do Carmo-Dajzcer surfaces (i.e., helicoidal constant mean curvature surfaces).
Cite
@article{arxiv.dg-ga/9505006,
title = {Constant mean curvature surfaces via integrable dynamical system},
author = {B. G. Konopelchenko and I. A. Taimanov},
journal= {arXiv preprint arXiv:dg-ga/9505006},
year = {2009}
}
Comments
9 pages, LaTeX