The spectral data for Hamiltonian stationary Lagrangian tori in R^4

Details The spectral data for Hamiltonian stationary Lagrangian tori in R^4 The spectral data for Hamiltonian stationary Lagrangian tori in R^4

2007-07-12

arxiv.org/abs/0707.1767v3

Differ.Geom.Appl.29:125-146,2011

Mathematics

Differential Geometry

30 pages. Version 3: a complete rewrite of version 2 with new results and two significant corrections

Scientific paper

10.1016/j.difgeo.2011.02.007

This article determines the spectral data, in the integrable systems sense, for all weakly conformally immersed Hamiltonian stationary Lagrangian in $\R^4$. This enables us to describe their moduli space and the locus of branch points of such an immersion. This is also an informative example in integrable systems geometry, since the group of ambient isometries acts non-trivially on the spectral data and the relevant energy functional (the area) need not be constant under deformations by higher flows.

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