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r-Harmonic and complex isoparametric functions on the Lie groups Rm⋉Rn and Rm⋉H2n+1

Gudmundsson, Sigmundur LU orcid and Sobak, Marko (2020) In Annals of Global Analysis and Geometry 58(4). 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 Rm⋉ Rn and Rm⋉ H 2n+1, where H 2n+1 denotes the classical (2 n+ 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
issue
4
pages
20 pages
publisher
Springer
external identifiers
  • scopus:85091254678
ISSN
1572-9060
DOI
10.1007/s10455-020-09736-3
language
English
LU publication?
yes
id
3d8a0e7b-f75f-4839-8a24-7e9398c145ca
date added to LUP
2020-10-09 14:08:09
date last changed
2022-05-19 07:45:17
@article{3d8a0e7b-f75f-4839-8a24-7e9398c145ca,
  abstract     = {{<p>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<sup>m</sup>⋉ R<sup>n</sup> and R<sup>m</sup>⋉ H <sup>2</sup><sup>n</sup><sup>+</sup><sup>1</sup>, where H <sup>2</sup><sup>n</sup><sup>+</sup><sup>1</sup> denotes the classical (2 n+ 1) -dimensional Heisenberg group. In particular, we construct such examples on all the simply connected irreducible four-dimensional Lie groups.</p>}},
  author       = {{Gudmundsson, Sigmundur and Sobak, Marko}},
  issn         = {{1572-9060}},
  keywords     = {{Biharmonic functions; Solvable Lie groups}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{4}},
  pages        = {{477--496}},
  publisher    = {{Springer}},
  series       = {{Annals of Global Analysis and Geometry}},
  title        = {{r-Harmonic and complex isoparametric functions on the Lie groups R<sup>m</sup>⋉R<sup>n</sup> and R<sup>m</sup>⋉H<sup>2</sup><sup>n</sup><sup>+</sup><sup>1</sup>}},
  url          = {{http://dx.doi.org/10.1007/s10455-020-09736-3}},
  doi          = {{10.1007/s10455-020-09736-3}},
  volume       = {{58}},
  year         = {{2020}},
}