Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912430594981888 |
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| author | Burstall, F. E. |
| author_facet | Burstall, F. E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type Burstall, F. E. Differential Geometry 58E20 (Primary), 53C35 (Secondary) 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. |
| title | Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type |
| topic | Differential Geometry 58E20 (Primary), 53C35 (Secondary) |
| url | https://arxiv.org/abs/2404.08596 |