On the geometry of harmonic morphisms
(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:
https://lup.lub.lu.se/record/1474724
- author
- Gudmundsson, Sigmundur LU
- organization
- publishing date
- 1990
- 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
- 2016-04-01 16:04:51
- date last changed
- 2021-08-01 04:17:22
@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}}, doi = {{10.1017/S0305004100069358}}, volume = {{108}}, year = {{1990}}, }