Harmonic spheres in outer symmetric spaces, their canonical elements and Weierstrass type representations

N. Correia; R. Pacheco

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arXiv · 1412.8348

Harmonic spheres in outer symmetric spaces, their canonical elements and Weierstrass type representations

N. Correia·R. Pacheco

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Abstract

Making use of Murakami's classification of outer involutions in a Lie algebra and following the Morse-theoretic approach to harmonic two-spheres in Lie groups introduced by Burstall and Guest, we obtain a new classification of harmonic two-spheres in outer symmetric spaces and a Weierstrass-type representation for such maps. Several examples of harmonic maps into classical outer symmetric spaces are given in terms of meromorphic functions on $S^2$.

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N. Correia, R. Pacheco. 2014-12-29. Harmonic spheres in outer symmetric spaces, their canonical elements and Weierstrass type representations. https://arxiv.org/abs/1412.8348

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