Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908463131525120 |
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| author | Gudmundsson, Sigmundur Munn, Thomas Jack |
| author_facet | Gudmundsson, Sigmundur Munn, Thomas Jack |
| contents | Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ of on $G$. We then show that the foliation $\F$ is Riemannian and minimal. This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups Gudmundsson, Sigmundur Munn, Thomas Jack Differential Geometry 53C35, 53C43, 58E20 Let $G$ be a Lie group equipped with a left-invariant Riemannian metric. Let $K$ be a semisimple and normal subgroup of $G$ generating a left-invariant conformal foliation $\F$ of on $G$. We then show that the foliation $\F$ is Riemannian and minimal. This means that locally the leaves of $\F$ are fibres of a harmonic morphism. We also prove that if the metric restricted to $K$ is biinvariant then $\F$ is totally geodesic. |
| title | Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups |
| topic | Differential Geometry 53C35, 53C43, 58E20 |
| url | https://arxiv.org/abs/2502.18492 |