The classification of Hamiltonian stationary Lagrangian tori in the complex projective plane by their spectral data

Details The classification of Hamiltonian stationary Lagrangian tori in the complex projective plane by their spectral data The classification of Hamiltonian stationary Lagrangian tori in the complex projective plane by their spectral data

2010-04-12

arxiv.org/abs/1004.1968v2

Mathematics

Differential Geometry

24 pages. Edited from the original to improve readability, and a new section on the explicit construction of examples included

Scientific paper

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.

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