Conformal foliations on Lie groups and complex-valued harmonic morphisms
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/15c66405-3b2f-43f6-88c0-3cc5c01f6728
- author
- Gudmundsson, Sigmundur
LU
; Ghandour, Elsa LU and Turner, Thomas
- organization
- publishing date
- 2021
- 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
- 2022-04-19 01:11:01
@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}}, }