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Harmonic morphisms from solvable Lie groups

Gudmundsson, Sigmundur LU orcid and Svensson, Martin LU (2009) In Mathematical Proceedings of the Cambridge Philosophical Society 147(2). p.389-408
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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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematical Proceedings of the Cambridge Philosophical Society
volume
147
issue
2
pages
389 - 408
publisher
Cambridge University Press
external identifiers
  • wos:000269277400009
  • scopus:70450247250
ISSN
1469-8064
DOI
10.1017/S0305004109002564
language
English
LU publication?
yes
id
724f4882-de69-47f9-bbac-808698eb225c (old id 1455132)
date added to LUP
2016-04-01 12:58:00
date last changed
2025-04-04 15:20:07
@article{724f4882-de69-47f9-bbac-808698eb225c,
  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.}},
  author       = {{Gudmundsson, Sigmundur and Svensson, Martin}},
  issn         = {{1469-8064}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{389--408}},
  publisher    = {{Cambridge University Press}},
  series       = {{Mathematical Proceedings of the Cambridge Philosophical Society}},
  title        = {{Harmonic morphisms from solvable Lie groups}},
  url          = {{http://dx.doi.org/10.1017/S0305004109002564}},
  doi          = {{10.1017/S0305004109002564}},
  volume       = {{147}},
  year         = {{2009}},
}