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arXiv · 1007.4477

Harmonic maps of finite uniton number into $G_2$

N. Correia·R. Pacheco
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Abstract

We establish explicit formulae for canonical factorizations of extended solutions corresponding to harmonic maps of finite uniton number into the exceptional Lie group $G_2$ in terms of the Grassmannian model for the group of based algebraic loops in $G_2$. A description of the ``Frenet frame data" for such harmonic maps is given. In particular, we show that harmonic spheres into $G_2$ correspond to solutions of certain algebraic systems of quadratic and cubic equations.

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N. Correia, R. Pacheco. 2010-07-26. Harmonic maps of finite uniton number into $G_2$. https://arxiv.org/abs/1007.4477

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