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

Richard Hunter, Ian McIntosh

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)437-468
Number of pages31
JournalManuscripta Mathematica
Volume135
Issue number3-4
Early online date1 Jan 2011
DOIs
Publication statusPublished - 1 Jul 2011

Keywords

  • Geometry, Pure Mathematics

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