English

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.

Keywords

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

R2 v1 2026-07-22T16:34:51.286Z