  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.
