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On the geometry of harmonic morphisms

Gudmundsson, Sigmundur LU (1990) In Mathematical Proceedings of the Cambridge Philosophical Society 108(3). p.461-466
Abstract
Let π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematical Proceedings of the Cambridge Philosophical Society
volume
108
issue
3
pages
461 - 466
publisher
Cambridge University Press
external identifiers
  • scopus:84972348081
ISSN
1469-8064
DOI
10.1017/S0305004100069358
language
English
LU publication?
yes
id
51dd7731-00f9-47d6-ab95-a680226f6ca7 (old id 1474724)
alternative location
http://journals.cambridge.org/download.php?file=%2FPSP%2FPSP108_03%2FS0305004100069358a.pdf&code=56018985e812666e91f4e05f6aebbcf2
date added to LUP
2009-09-18 10:39:54
date last changed
2017-09-17 07:07:55
@article{51dd7731-00f9-47d6-ab95-a680226f6ca7,
  abstract     = {Let π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.},
  author       = {Gudmundsson, Sigmundur},
  issn         = {1469-8064},
  language     = {eng},
  number       = {3},
  pages        = {461--466},
  publisher    = {Cambridge University Press},
  series       = {Mathematical Proceedings of the Cambridge Philosophical Society},
  title        = {On the geometry of harmonic morphisms},
  url          = {http://dx.doi.org/10.1017/S0305004100069358},
  volume       = {108},
  year         = {1990},
}