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Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds

Gudmundsson, Sigmundur LU (2015) In International Journal of Mathematics 26(1).
Abstract
We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not Kähler. We then prove that the Riemannian Lie groups constructed are not Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
harmonic morphisms, holomorphic foliations, Einstein manifolds
in
International Journal of Mathematics
volume
26
issue
1
publisher
World Scientific
external identifiers
  • wos:000351093200006
  • scopus:84928379357
ISSN
0129-167X
DOI
10.1142/S0129167X15500068
language
English
LU publication?
yes
id
78e70e8f-689c-49bc-b160-2ef28e0a4c53 (old id 4448095)
date added to LUP
2015-01-26 13:31:16
date last changed
2017-03-13 14:13:00
@article{78e70e8f-689c-49bc-b160-2ef28e0a4c53,
  abstract     = {We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not Kähler. We then prove that the Riemannian Lie groups constructed are not Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.},
  articleno    = {1550006},
  author       = {Gudmundsson, Sigmundur},
  issn         = {0129-167X},
  keyword      = {harmonic morphisms,holomorphic foliations,Einstein manifolds},
  language     = {eng},
  number       = {1},
  publisher    = {World Scientific},
  series       = {International Journal of Mathematics},
  title        = {Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds},
  url          = {http://dx.doi.org/10.1142/S0129167X15500068},
  volume       = {26},
  year         = {2015},
}