Hamiltonian stationary Lagrangian surfaces in C^2
Differential Geometry
2007-05-23 v1
Abstract
We study Hamiltonian stationary Lagrangian surfaces in C^2, i.e. Lagrangian surfaces in C^2 which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representation and produce all tori through either the integrable systems machinery or more direct arguments.
Cite
@article{arxiv.math/0009202,
title = {Hamiltonian stationary Lagrangian surfaces in C^2},
author = {Frederic Helein and Pascal Romon},
journal= {arXiv preprint arXiv:math/0009202},
year = {2007}
}
Comments
3 figures