Harmonic morphisms as unit normal bundles¶of minimal surfaces

Abstract

Let \(\) be an isometric immersion between Riemannian manifolds and \(\) be the unit normal bundle of f. We discuss two natural Riemannian metrics on the total space \(\) and necessary and sufficient conditions on f for the projection map \(\) to be a harmonic morphism. We show that the projection map of the unit normal bundle of a minimal surface in a Riemannian manifold is a harmonic morphism with totally geodesic fibres.