Harmonic morphisms on Lie groups and minimal conformal foliations of codimension two
Gudmundsson, Sigmundur LU
and Munn, Thomas Jack
LU
(2024)
In Journal of Geometry and Physics
198.
- Abstract
Let G be a Lie group equipped with a left-invariant semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This means that locally the leaves of F are fibres of a complex-valued harmonic morphism. In the Riemannian case, we 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:
https://lup.lub.lu.se/record/02dbc9a1-fa53-4ccb-aae6-91d8115c8c83
- author
- Gudmundsson, Sigmundur
LU
and Munn, Thomas Jack
LU
- organization
- publishing date
- 2024-04
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Conformal and minimal foliations, Harmonic morphisms, Lie groups
- in
- Journal of Geometry and Physics
- volume
- 198
- article number
- 105130
- publisher
- Elsevier
- external identifiers
-
- scopus:85184003907
- ISSN
- 0393-0440
- DOI
- 10.1016/j.geomphys.2024.105130
- language
- English
- LU publication?
- yes
- id
- 02dbc9a1-fa53-4ccb-aae6-91d8115c8c83
- date added to LUP
- 2024-02-22 15:24:16
- date last changed
- 2024-02-22 15:25:18
@article{02dbc9a1-fa53-4ccb-aae6-91d8115c8c83,
abstract = {{<p>Let G be a Lie group equipped with a left-invariant semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This means that locally the leaves of F are fibres of a complex-valued harmonic morphism. In the Riemannian case, we prove that if the metric restricted to K is biinvariant then F is totally geodesic.</p>}},
author = {{Gudmundsson, Sigmundur and Munn, Thomas Jack}},
issn = {{0393-0440}},
keywords = {{Conformal and minimal foliations; Harmonic morphisms; Lie groups}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Journal of Geometry and Physics}},
title = {{Harmonic morphisms on Lie groups and minimal conformal foliations of codimension two}},
url = {{http://dx.doi.org/10.1016/j.geomphys.2024.105130}},
doi = {{10.1016/j.geomphys.2024.105130}},
volume = {{198}},
year = {{2024}},
}