Harmonic morphisms between spaces of constant curvature
Author
Summary, in English
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.
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.
Department/s
- Differential Geometry
Publishing year
1993
Language
English
Pages
133-143
Publication/Series
Proceedings of the Edinburgh Mathematical Society
Volume
36
Links
Document type
Journal article
Publisher
Cambridge University Press
Topic
- Geometry
Status
Published
Research group
- Differential Geometry
ISBN/ISSN/Other
- ISSN: 1464-3839