Harmonic morphisms from solvable Lie groups
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1455132
- author
- Gudmundsson, Sigmundur
LU
and Svensson, Martin LU
- organization
- publishing date
- 2009
- 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}}, }