Elliptic Integrable Systems: a Comprehensive Geometric Interpretation

Details Elliptic Integrable Systems: a Comprehensive Geometric Interpretation Elliptic Integrable Systems: a Comprehensive Geometric Interpretation

2009-04-08

arxiv.org/abs/0904.1412v6

Mathematics

Differential Geometry

Scientific paper

We give a geometric interpretation of all the $m$-th elliptic integrable systems associated to a $k'$-symmetric space $N=G/G_0$ (in the sense of C.L. Terng). It turns out that we have to introduce the integer $m_{k'}$ defined by m_{1}=0 and m_{k'}= [(k'+1)/2]. Then the general problem splits into three cases : the primitive case ($m < m_{k'}$), the determined case ($m_{k'}\leq m \leq k'-1$) and the underdetermined case ($m \geq k'$). 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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