Harmonic morphisms between spaces of constant curvature
Författare
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.
Avdelning/ar
- Differential Geometry
Publiceringsår
1993
Språk
Engelska
Sidor
133-143
Publikation/Tidskrift/Serie
Proceedings of the Edinburgh Mathematical Society
Volym
36
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Cambridge University Press
Ämne
- Geometry
Status
Published
Forskningsgrupp
- Differential Geometry
ISBN/ISSN/Övrigt
- ISSN: 1464-3839