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Harmonic morphisms from solvable Lie groups

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Author

Summary, in English

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.

Department/s

Publishing year

2009

Language

English

Pages

389-408

Publication/Series

Mathematical Proceedings of the Cambridge Philosophical Society

Volume

147

Issue

2

Document type

Journal article

Publisher

Cambridge University Press

Topic

  • Geometry

Status

Published

Research group

  • Differential Geometry

ISBN/ISSN/Other

  • ISSN: 1469-8064