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Abstract 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.
Francis E. Burstall (Wed,) studied this question.