‘the Classification of Hamiltonian Stationary Lagrangian Tori in Cp^2 by Their Spectral Data’

It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in CP 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 CP, 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.