Some examples of `second order elliptic integrable systems associated to a 4-symmetric space'

Details Some examples of `second order elliptic integrable systems associated to a 4-symmetric space' Some examples of `second order elliptic integrable systems associated to a 4-symmetric space'

2008-12-12

arxiv.org/abs/0812.2348v1

Physics

Mathematical Physics

London Mathematical Society Durham symposium : Methods of Integrable Systems in Geometry, Durham : Royaume-Uni (2006)

Scientific paper

In this text we expound recent results by Idrisse Khemar on the construction of various geometric completely integrable systems generalizing the structure of Hamiltonian stationary Lagrangian surfaces (HSLS) discovered by F. H\'elein and P. Romon. We first explain that, for surfaces in a 4-dimensional Euclidean space, the HSLS are a particular case of a more general theory of surfaces with harmonic left Gauss map and that this theory includes also the classical constant mean curvature surfaces in 3-space. Then we expound a generalization of this theory for surfaces in an 8-dimensional Euclidean space, using octonions. Lastly we discuss supersymmetric harmonic and primitive maps, a theory which also covers the HSLS cas.

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