Harmonic morphisms between spaces of constant curvature
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 horizontal
