Abstract
It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in \({{\mathbb {CP}}^2}\) may be constructed by methods from integrable systems theory. This article describes the precise details of a construction which leads to a form of classification. The immersion is encoded as spectral data in a similar manner to the case of minimal Lagrangian tori in \({{\mathbb {CP}}^2}\) , but the details require a careful treatment of both the “dressing construction” and the spectral data to deal with a loop of flat connexions which is quadratic in the loop parameter.
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Hunter, R., McIntosh, I. The classification of Hamiltonian stationary Lagrangian tori in \({{\mathbb {CP}}^2}\) by their spectral data. manuscripta math. 135, 437–468 (2011). https://doi.org/10.1007/s00229-010-0425-6
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DOI: https://doi.org/10.1007/s00229-010-0425-6