Elliptic Integrable Systems: a Comprehensive Geometric Interpretation

2009/04/08 by Idrisse Khemar, Khemar, Idrisse
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.0904.1412

arxiv created 2011/04/15 · arxiv updated 2011/04/18

Abstract

We give a geometric interpretation of all the m-th elliptic integrable systems associated to a k'-symmetric space N=G/G₀ (in the sense of C.L. Terng). It turns out that we have to introduce the integer m_k' defined by m₁=0 and m_k'= [(k'+1)/2]. Then the general problem splits into three cases : the primitive case (m < m_k'), the determined case (m_k'≤ m ≤ k'-1) and the underdetermined case (m ≥ k'). We prove that we have an interpretation in terms of a sigma model with a Wess-Zumino term. Moreover we prove that we have a geometric interpretation in terms of twistors. See the abstract in the paper for more precisions.

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