Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type
arXiv:2404.08596 · doi:10.1112/blms.13155
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 non-constant, 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.
7 A4 pages