ON THE GEOMETRY OF HARMONIC MORPHISMS

Let n :M→B be a horizontally conformai submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformai 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. © 1990, Cambridge Philosophical Society. All rights reserved.