Harmonic morphisms of warped product type from Einstein manifolds (Q882546)

The topic of this paper are harmonic morphisms of warped product type, i.e.\ non-constant horizontally homothetic maps between Riemannian manifolds with totally geodesic fibres and integrable horizontal distributions. There is an alternative characterization in terms of usual warped product structures. For such morphisms, Weitzenböck type identities are established. Their consequences concerning non-existence of certain harmonic morphisms are studied, mainly for domains which are Einstein manifolds. A common feature of all of these results is that they exclude harmonic morphisms of non-constant dilation under certain geometric assumptions on domain and target.