A Weierstrass-type representation for Lagrangian surfaces in R^4
Romon, Pascal
HAL, hal-00858084 / Harvested from HAL
Text on HAL
We derive a Weierstrass-type formula for conformal Lagrangian immersions in complex Euclidean 2-space, and show that the data satisfies a Dirac-type equation with complex potential. We apply the representation to the Hamiltonian-stationary case to construct all possible tori and obtain a first approach to a moduli space in terms of a simple algebraic-geometric problem on the plane. Results described here are contained in two articles in collaboration with Frédéric Hélein.
Publié le : 2000-07-05
Classification:  Weierstrass representation formula,  lagrangian surfaces,  Dirac equation,  hamiltonian stationary tori,  MSC : Primary 53D12, Secondary 53C42, 49Q10, 53A05,  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 
@article{hal-00858084,
     author = {Romon, Pascal},
     title = {A Weierstrass-type representation for Lagrangian surfaces in R^4},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00858084}
}

Romon, Pascal. A Weierstrass-type representation for Lagrangian surfaces in R^4. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00858084/