Hamiltonian stationary Lagrangian surfaces in C^2

Details Hamiltonian stationary Lagrangian surfaces in C^2 Hamiltonian stationary Lagrangian surfaces in C^2

2000-09-22

arxiv.org/abs/math/0009202v1

Mathematics

Differential Geometry

3 figures

Scientific paper

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.

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