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The classification of Hamiltonian stationary Lagrangian tori in CP^2 by their spectral data.

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Publication details

JournalManuscripta Mathematica
DateE-pub ahead of print - 1 Jan 2011
DatePublished (current) - 1 Jul 2011
Issue number3-4
Volume135
Number of pages31
Pages (from-to)437-468
Early online date1/01/11
Original languageEnglish

Abstract

It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in the complex projective plane 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 the complex projective plane, 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.

    Research areas

  • Geometry, Pure Mathematics

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