Harmonic morphisms between spaces of constant curvature
(1993) In Proceedings of the Edinburgh Mathematical Society 36. p.133143 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:
http://lup.lub.lu.se/record/1474725
 author
 Gudmundsson, Sigmundur ^{LU}
 organization
 publishing date
 1993
 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
 14643839
 language
 English
 LU publication?
 yes
 id
 a59a5040fcc947c0a45326ea7067c085 (old id 1474725)
 alternative location
 http://journals.cambridge.org/download.php?file=%2FPEM%2FPEM2_36_01%2FS0013091500005940a.pdf&code=8955e6625394f3ecae713db408d36660
 date added to LUP
 20090918 11:05:23
 date last changed
 20180107 10:24:38
@article{a59a5040fcc947c0a45326ea7067c085, 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 = {14643839}, language = {eng}, pages = {133143}, publisher = {Cambridge University Press}, series = {Proceedings of the Edinburgh Mathematical Society}, title = {Harmonic morphisms between spaces of constant curvature}, volume = {36}, year = {1993}, }