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

Ian McIntosh

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

Mathematics

Research output: Contribution to conference › Other

Abstract

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 language	English
Pages	163-184
Publication status	Published - 2007
Event	Symposium on the differential geometry of submanifolds - Valenciennes, France Duration: 3 Jul 2007 → 7 Jul 2007

Conference

Conference	Symposium on the differential geometry of submanifolds
Country/Territory	France
City	Valenciennes
Period	3/07/07 → 7/07/07

Cite this

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title = "Hamiltonian stationary Lagrangian tori in R^4 and CP^2",

abstract = "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.",

author = "Ian McIntosh",

year = "2007",

language = "English",

pages = "163--184",

note = "Symposium on the differential geometry of submanifolds ; Conference date: 03-07-2007 Through 07-07-2007",

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TY - CONF

T1 - Hamiltonian stationary Lagrangian tori in R^4 and CP^2

AU - McIntosh, Ian

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

M3 - Other

SP - 163

EP - 184

T2 - Symposium on the differential geometry of submanifolds

Y2 - 3 July 2007 through 7 July 2007

ER -