Hamiltonian stationary Lagrangian tori in R^4 and CP^2

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This article summarises the contribution integrable systems methods can make to the construction and classification of weakly conformal Hamiltonian stationary Lagrangian immersions of tori in R^4 and CP^2. There is an explicit and complete description of the construction and moduli spaces, for each conformal class of torus and choice of Maslov class, in the case of R^4. For CP^2 there is a less practical, but in principle complete, classification. In both cases the immersion is encoded into spectral data in a manner now familiar for geometries which admit an integrable systems approach.
Original languageEnglish
Publication statusPublished - 2007
EventSymposium on the differential geometry of submanifolds - Valenciennes, France
Duration: 3 Jul 20077 Jul 2007


ConferenceSymposium on the differential geometry of submanifolds

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