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Harmonic morphisms from the classical non-compact semisimple Lie groups

Gudmundsson, Sigmundur LU and Sakovich, Anna (2009) In Differential Geometry and its Applications 27(1). p.47-63
Abstract
We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups View the MathML source, SU*(2n) and View the MathML source equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Harmonic morphisms, Minimal submanifolds, Lie groups
in
Differential Geometry and its Applications
volume
27
issue
1
pages
47 - 63
publisher
North-Holland
external identifiers
  • wos:000263214000006
  • scopus:58149382441
ISSN
1872-6984
DOI
10.1016/j.difgeo.2008.10.003
language
English
LU publication?
yes
id
afda8ff2-590f-4ca2-ac25-014efd5b1e88 (old id 829679)
date added to LUP
2009-05-19 14:39:58
date last changed
2017-03-13 14:13:01
@article{afda8ff2-590f-4ca2-ac25-014efd5b1e88,
  abstract     = {We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups View the MathML source, SU*(2n) and View the MathML source equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.},
  author       = {Gudmundsson, Sigmundur and Sakovich, Anna},
  issn         = {1872-6984},
  keyword      = {Harmonic morphisms,Minimal submanifolds,Lie groups},
  language     = {eng},
  number       = {1},
  pages        = {47--63},
  publisher    = {North-Holland},
  series       = {Differential Geometry and its Applications},
  title        = {Harmonic morphisms from the classical non-compact semisimple Lie groups},
  url          = {http://dx.doi.org/10.1016/j.difgeo.2008.10.003},
  volume       = {27},
  year         = {2009},
}