Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type

We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank‐one totally geodesic subspaces. Among the consequences, we prove the existence of a nonconstant, globally defined complex‐valued harmonic morphism from the Riemannian symmetric space associated to a split real semisimple Lie group. This completes an affirmative proof of a conjecture of Gudmundsson.