New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n)
Gudmundsson, Sigmundur LU
and Siffert, Anna
(2021)
In Journal of Geometric Analysis
31(1).
p.250-281
- Abstract
- We develop a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special unitary group SU(n). We then show that the special orthogonal group SO(n) and the quaternionic unitary group Sp(n) fall into the scheme. As a by-product we obtain new harmonic morphisms on these groups. All the constructed maps are defined on open and dense subsets of the corresponding spaces.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9bfd9673-3880-44a7-9ae3-78e499368524
- author
- Gudmundsson, Sigmundur
LU
and Siffert, Anna
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Biharmonic functions, Compact simple Lie groups
- in
- Journal of Geometric Analysis
- volume
- 31
- issue
- 1
- pages
- 32 pages
- publisher
- Springer
- external identifiers
-
- scopus:85072081517
- ISSN
- 1559-002X
- DOI
- 10.1007/s12220-019-00259-3
- language
- English
- LU publication?
- yes
- id
- 9bfd9673-3880-44a7-9ae3-78e499368524
- date added to LUP
- 2020-01-15 13:53:10
- date last changed
- 2025-04-04 14:17:55
@article{9bfd9673-3880-44a7-9ae3-78e499368524,
abstract = {{We develop a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special unitary group SU(n). We then show that the special orthogonal group SO(n) and the quaternionic unitary group Sp(n) fall into the scheme. As a by-product we obtain new harmonic morphisms on these groups. All the constructed maps are defined on open and dense subsets of the corresponding spaces. <br/>}},
author = {{Gudmundsson, Sigmundur and Siffert, Anna}},
issn = {{1559-002X}},
keywords = {{Biharmonic functions; Compact simple Lie groups}},
language = {{eng}},
number = {{1}},
pages = {{250--281}},
publisher = {{Springer}},
series = {{Journal of Geometric Analysis}},
title = {{New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n)}},
url = {{http://dx.doi.org/10.1007/s12220-019-00259-3}},
doi = {{10.1007/s12220-019-00259-3}},
volume = {{31}},
year = {{2021}},
}