Harmonic morphisms from the classical compact semisimple Lie groups |
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Authors: | Sigmundur Gudmundsson Anna Sakovich |
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Affiliation: | (1) Mathematics, Faculty of Science, Lund University, Box 118, Lund, 221, Sweden;(2) Faculty of Pre-University Preparation, Belarusian State University, Oktyabrskaya Str. 4, Minsk, 220030, Belarus |
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Abstract: | In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups , SU *(2n), , SO *(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics. |
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Keywords: | Harmonic morphisms Minimal submanifolds Lie groups |
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