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Harmonic morphisms from solvable Lie groups

Published online by Cambridge University Press:  01 September 2009

SIGMUNDUR GUDMUNDSSON  and
MARTIN SVENSSON
SIGMUNDUR GUDMUNDSSON
Affiliation:
Department of Mathematics, Faculty of Science, Lund University, Box 118, S-22100 Lund, Sweden. e-mail: Sigmundur.Gudmundsson@math.lu.se
MARTIN SVENSSON
Affiliation:
Department of Mathematics & Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. e-mail: svensson@imada.sdu.dk
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Abstract

In this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of non-compact type and rank r ≥ 3. The second method provides us with global solutions from any Damek–Ricci space and many non-compact Riemannian symmetric spaces. We then give a continuous family of 3-dimensional solvable Lie groups not admitting any complex-valued harmonic morphisms, not even locally.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 389 - 408
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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