Constant mean curvature surfaces via integrable dynamical system

Details Constant mean curvature surfaces via integrable dynamical system Constant mean curvature surfaces via integrable dynamical system

1995-05-26

arxiv.org/abs/dg-ga/9505006v1

J. Phys. A 29 (1996), 1261--1265.

Mathematics

Differential Geometry

9 pages, LaTeX

Scientific paper

10.1088/0305-4470/29/6/012

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).

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