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Harmonic morphisms from the classical non-compact semisimple Lie groups
Belarusian State University. (Faculty of Pre-University Preparation)
Lund University. (Mathematics, Faculty of science)
2009 (English)In: Differential geometry and its applications (Print), ISSN 0926-2245, E-ISSN 1872-6984, Vol. 27, no 1, 47-63 p.Article in journal (Refereed) Published
Abstract [en]

We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups SL(n) (R), SU*(2n) and Sp(n, R) equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p, q), SU(p, q) and Sp(p, q). Applying a duality, principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.

Place, publisher, year, edition, pages
2009. Vol. 27, no 1, 47-63 p.
Keyword [en]
Harmonic morphisms, Minimal submanifolds, Lie groups
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-67478DOI: 10.1016/j.difgeo.2008.10.003ISI: 000263214000006OAI: oai:DiVA.org:kth-67478DiVA: diva2:485025
Note
QC 20120130Available from: 2012-01-27 Created: 2012-01-27 Last updated: 2017-12-08Bibliographically approved

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