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Communication Dans Un Congrès Tohoku mathematical journal Année : 2001

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

Résumé

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.
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Dates et versions

hal-00858084 , version 1 (04-09-2013)

Identifiants

  • HAL Id : hal-00858084 , version 1

Citer

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⟩
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