%0 Journal Article
%T Geometric Interpretation of Second Elliptic Integrable System
%A Idrisse Khemar
%J Mathematics
%D 2008
%I arXiv
%X In this paper we give a geometrical interpretation of all the second elliptic integrable systems associated to 4-symmetric spaces. We first show that a 4-symmetric space $G/G_0$ can be embedded into the twistor space of the corresponding symmetric space $G/H$. Then we prove that the second elliptic system is equivalent to the vertical harmonicity of an admissible twistor lift $J$ taking values in $G/G_0 \hookrightarrow \Sigma(G/H)$. We begin the paper by an example: $G/H=\R^4$. We study also the structure of 4-symmetric bundles over Riemannian symmetric spaces.
%U http://arxiv.org/abs/0803.3341v3