2008/12/12 by Frédéric Hélein, Hélein, Frédéric
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0812.2348
openalex publication_date 2008/12/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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. Hélein 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.