A Weierstrass-type representation for Lagrangian surfaces in R^4

Pascal Romon (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Weierstrass representation formula; lagrangian surfaces; Dirac equation; hamiltonian stationary tori

Domaines: Géométrie différentielle [math.DG]

Pascal Romon. A Weierstrass-type representation for Lagrangian surfaces in R^4. Fifth Pacific Rim Geometry Conference, 2000, Sendai, Japan. pp.147-152. ⟨hal-00858084⟩