Harmonic maps of finite uniton number into $G_2$

Details Harmonic maps of finite uniton number into $G_2$ Harmonic maps of finite uniton number into $G_2$

2010-07-26

arxiv.org/abs/1007.4477v1

Mathematics

Differential Geometry

Scientific paper

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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