
The spectral data for Hamiltonian stationary Lagrangian tori in R^4
Title  The spectral data for Hamiltonian stationary Lagrangian tori in R^4 
Publication Type  Journal Article 
Year of Publication  2011 
Authors  McIntosh I, Romon P 
Journal  Differential Geometry and its Applications 
Volume  29 
Start Page  125 
Issue  2 
Date Published  03/2011 
Abstract  Hamiltonian stationary Lagrangian submanifolds are solutions of a natural and important variational problem in Kaehler geometry. In the particular case of surfaces in Euclidean 4space, it has recently been proved that the EulerLagrange equation is a completely integrable system, which theory allows us to describe all such tori. This article determines the spectral data for these, in terms of a complete algebraic curve, a rational function and a line bundle. We use this data to give explicit formulas for all weakly conformal HSL immersions of a 2torus into Euclidean 4space and describe the moduli space of those with given conformal type and Maslov class. We also show that each such torus admits a family of Hamiltonian deformations through HSL tori, the dimension of this family being related to the genus of its spectral curve.

URL  http://www.sciencedirect.com/science/journal/09262245 
DOI  doi:10.1016/j.difgeo.2011.02.007 
Eprint number  arXiv:0707.1767

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Edited 22 Jun 2011  11:07 by im7
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