Geometric Interpretation of Second Elliptic Integrable System

2008/03/23 by Idrisse Khemar, Khemar, Idrisse
Mathematics · #35J #53A #53C #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35J #msc:53A #msc:53C

paper · pdf · doi:10.48550/arxiv.0803.3341

arxiv created 2009/04/09 · arxiv updated 2009/12/01

Abstract

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/G₀ 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/G₀ \hookrightarrow Σ(G/H). We begin the paper by an example: G/H=\R⁴. We study also the structure of 4-symmetric bundles over Riemannian symmetric spaces.

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