Hamiltonian stationary Lagrangian surfaces in C^2

Hélein, Frédéric; Romon, Pascal

HAL, hal-00795181 / Harvested from HAL

Résumé

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.

Publié le : 2002-07-05
Classification: completely integrable systems, Lagrangian surfaces, minimal Lagrangian surfaces, harmonic maps, loop groups, primary 53C42, secondary 58E20, 58F07, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]

@article{hal-00795181,
     author = {H\'elein, Fr\'ed\'eric and Romon, Pascal},
     title = {Hamiltonian stationary Lagrangian surfaces in C^2},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00795181}
}

Hélein, Frédéric; Romon, Pascal. Hamiltonian stationary Lagrangian surfaces in C^2. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00795181/