English

Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type

Differential Geometry 2025-06-17 v1

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.

Keywords

Cite

@article{arxiv.2404.08596,
  title  = {Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type},
  author = {F. E. Burstall},
  journal= {arXiv preprint arXiv:2404.08596},
  year   = {2025}
}

Comments

7 A4 pages