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

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• 作者：N. Correia ; R. Pacheco
• 关键词：Mathematics Subject Classification58E20 ; 53C35 ; 53C43
• 刊名：manuscripta mathematica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：152
• 期：3-4
• 页码：399-432
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1785
• 卷排序：152

文摘

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 \(S^2\).