Harmonic morphisms between spaces of constant curvature
(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:
https://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
- 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}}, }