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Harmonic morphisms and minimal conformal foliations on Lie groups

Gudmundsson, Sigmundur LU orcid and Munn, Thomas LU orcid (2025) In Annals of Global Analysis and Geometry 68.
Abstract
Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ on $G$. We then show that the foliation $\F$ is Riemannian and minimal. This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Harmonic morphisms, Lie groups, Conformal and minimal foliations
in
Annals of Global Analysis and Geometry
volume
68
article number
11
pages
15 pages
publisher
Springer
external identifiers
  • scopus:105014900324
ISSN
1572-9060
DOI
10.1007/s10455-025-10015-2
language
English
LU publication?
yes
id
b50a53fd-82c6-4cca-9950-78a4c135b069
date added to LUP
2025-09-02 20:24:01
date last changed
2025-10-25 04:01:56
@article{b50a53fd-82c6-4cca-9950-78a4c135b069,
  abstract     = {{Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ on $G$.  We then show that the foliation $\F$ is Riemannian and minimal.  This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic.}},
  author       = {{Gudmundsson, Sigmundur and Munn, Thomas}},
  issn         = {{1572-9060}},
  keywords     = {{Harmonic morphisms; Lie groups; Conformal and minimal foliations}},
  language     = {{eng}},
  month        = {{08}},
  publisher    = {{Springer}},
  series       = {{Annals of Global Analysis and Geometry}},
  title        = {{Harmonic morphisms and minimal conformal foliations on Lie groups}},
  url          = {{http://dx.doi.org/10.1007/s10455-025-10015-2}},
  doi          = {{10.1007/s10455-025-10015-2}},
  volume       = {{68}},
  year         = {{2025}},
}