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Harmonic morphisms between spaces of constant curvature

Gudmundsson, Sigmundur LU (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?
no
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
2009-09-18 11:05:23
date last changed
2017-01-29 04:20:26
@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},
  volume       = {36},
  year         = {1993},
}