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Harmonic maps of finite uniton number into G 2

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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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  1. Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã, Portugal

    N. Correia & R. Pacheco

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  1. N. Correia
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  2. R. Pacheco
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Correspondence to R. Pacheco.

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Correia, N., Pacheco, R. Harmonic maps of finite uniton number into G 2 . Math. Z. 271, 13–32 (2012). https://doi.org/10.1007/s00209-011-0849-z

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  • DOI: https://doi.org/10.1007/s00209-011-0849-z

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