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Harmonic morphisms between spaces of constant curvature

Gudmundsson, Sigmundur LU orcid (1993) In Proceedings of the Edinburgh Mathematical Society 36. p.133-143
Abstract
Let M and N be simply connected space forms, and U an open and connected subset of M. Further let

n: U-*N be a horizontally homothetic harmonic morphism. In this paper we show that if n has totally

geodesic fibres and integrable horizontal distribution, then the horizontal foliation of U is totally umbilic and

isoparametric. This leads to a classification of such maps. We also show that horizontally homothetic

harmonic morphisms of codimension one are either Riemannian submersions modulo a constant, or up to

isometries of M and N one of six well known examples.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Proceedings of the Edinburgh Mathematical Society
volume
36
pages
133 - 143
publisher
Cambridge University Press
external identifiers
  • scopus:84976114766
ISSN
1464-3839
language
English
LU publication?
yes
id
a59a5040-fcc9-47c0-a453-26ea7067c085 (old id 1474725)
alternative location
http://journals.cambridge.org/download.php?file=%2FPEM%2FPEM2_36_01%2FS0013091500005940a.pdf&code=8955e6625394f3ecae713db408d36660
date added to LUP
2016-04-04 09:36:19
date last changed
2021-09-26 05:25:47
@article{a59a5040-fcc9-47c0-a453-26ea7067c085,
  abstract     = {{Let M and N be simply connected space forms, and U an open and connected subset of M. Further let<br/><br>
n: U-*N be a horizontally homothetic harmonic morphism. In this paper we show that if n has totally<br/><br>
geodesic fibres and integrable horizontal distribution, then the horizontal foliation of U is totally umbilic and<br/><br>
isoparametric. This leads to a classification of such maps. We also show that horizontally homothetic<br/><br>
harmonic morphisms of codimension one are either Riemannian submersions modulo a constant, or up to<br/><br>
isometries of M and N one of six well known examples.}},
  author       = {{Gudmundsson, Sigmundur}},
  issn         = {{1464-3839}},
  language     = {{eng}},
  pages        = {{133--143}},
  publisher    = {{Cambridge University Press}},
  series       = {{Proceedings of the Edinburgh Mathematical Society}},
  title        = {{Harmonic morphisms between spaces of constant curvature}},
  url          = {{http://journals.cambridge.org/download.php?file=%2FPEM%2FPEM2_36_01%2FS0013091500005940a.pdf&code=8955e6625394f3ecae713db408d36660}},
  volume       = {{36}},
  year         = {{1993}},
}