Hamiltonian stationary Lagrangian surfaces in C^2

Frederic Helein; Pascal Romon

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Hamiltonian stationary Lagrangian surfaces in C^2

Frederic Helein·Pascal Romon

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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.

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BibTeX RIS

Frederic Helein, Pascal Romon. 2000-09-22. Hamiltonian stationary Lagrangian surfaces in C^2. https://arxiv.org/abs/math/0009202

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