We obtain a characterization of totally geodesic horizontally conformal
maps by a method which arises as a consequence of the Bochner technique
for harmonic morphisms. As a geometric consequence we show that the
existence of a non-constant harmonic morphism $\textrm{Ø}$ from a
compact Riemannian manifold M$^{m}$ of non-negative Ricci curvature
to a compact Riemannian manifold of non-positive scalar curvature,
forces M$^{m}$ either to be a global Riemannian product of integral
manifolds of vertical and horizontal distributions or to be covered
by a global Riemannian product.
