Harmonic morphisms from solvable Lie groups

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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.

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  • Mathematics
Original languageEnglish
Pages (from-to)389-408
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume147
Issue number2
Publication statusPublished - 2009
Publication categoryResearch
Peer-reviewedYes