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Conformal foliations on Lie groups and complex-valued harmonic morphisms

Gudmundsson, Sigmundur LU orcid ; Ghandour, Elsa LU and Turner, Thomas (2021) In Journal of Geometry and Physics 159.
Abstract
We study left-invariant foliations F on Riemannian Lie groups G generated by a subgroup K. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations F when the subgroup K is one of the important SU(2)*SU(2), SU(2)*SL_2(R), SU(2)*SO(2) or SL_2(R)*SO(2). By this we yield new multi-dimensional families of Lie groups G carrying such foliations in each case. These foliations F produce local complex-valued harmonic morphisms on the corresponding Lie group G.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
conformal foliations, minimal submanifolds, harmonic morphisms
in
Journal of Geometry and Physics
volume
159
article number
103940
pages
11 pages
publisher
Elsevier
external identifiers
  • scopus:85092177671
ISSN
0393-0440
DOI
10.1016/j.geomphys.2020.103940
language
English
LU publication?
yes
id
15c66405-3b2f-43f6-88c0-3cc5c01f6728
date added to LUP
2020-10-09 15:04:19
date last changed
2025-10-14 11:27:38
@article{15c66405-3b2f-43f6-88c0-3cc5c01f6728,
  abstract     = {{We study left-invariant foliations F on Riemannian Lie groups G generated by a subgroup K. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations F when the subgroup K is one of the important SU(2)*SU(2), SU(2)*SL_2(R), SU(2)*SO(2) or SL_2(R)*SO(2). By this we yield new multi-dimensional families of Lie groups G carrying such foliations in each case. These foliations F produce local complex-valued harmonic morphisms on the corresponding Lie group G.}},
  author       = {{Gudmundsson, Sigmundur and Ghandour, Elsa and Turner, Thomas}},
  issn         = {{0393-0440}},
  keywords     = {{conformal foliations; minimal submanifolds; harmonic morphisms}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Geometry and Physics}},
  title        = {{Conformal foliations on Lie groups and complex-valued harmonic morphisms}},
  url          = {{http://dx.doi.org/10.1016/j.geomphys.2020.103940}},
  doi          = {{10.1016/j.geomphys.2020.103940}},
  volume       = {{159}},
  year         = {{2021}},
}