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r-Harmonic and Complex Isoparametric Functions on the Lie Groups R^m⋉R^n and R^m⋉H^(2n+1)

Gudmundsson, Sigmundur LU and Sobak, Marko (2020) In Annals of Global Analysis and Geometry 58. p.477-496
Abstract
In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products R^m⋉R^n and Rm⋉H^(2n+1), where H^(2n+1) denotes the classical (2n+1)-dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Biharmonic functions, Solvable Lie groups
in
Annals of Global Analysis and Geometry
volume
58
pages
20 pages
publisher
Springer
ISSN
1572-9060
language
English
LU publication?
yes
id
3d8a0e7b-f75f-4839-8a24-7e9398c145ca
date added to LUP
2020-10-09 14:08:09
date last changed
2021-04-04 22:28:12
@article{3d8a0e7b-f75f-4839-8a24-7e9398c145ca,
  abstract     = {In this paper we introduce the notion of complex isoparametric functions on Riemannian manifolds. These are then employed to devise a general method for constructing proper r-harmonic functions. We then apply this to construct the first known explicit proper r-harmonic functions on the Lie group semidirect products R^m⋉R^n and Rm⋉H^(2n+1), where H^(2n+1) denotes the classical (2n+1)-dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.},
  author       = {Gudmundsson, Sigmundur and Sobak, Marko},
  issn         = {1572-9060},
  language     = {eng},
  month        = {09},
  pages        = {477--496},
  publisher    = {Springer},
  series       = {Annals of Global Analysis and Geometry},
  title        = {r-Harmonic and Complex Isoparametric Functions on the Lie Groups R^m⋉R^n and R^m⋉H^(2n+1)},
  volume       = {58},
  year         = {2020},
}