Harmonic Morphisms on Lie groups and Minimal Conformal Foliations of Codimension two
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911819219599360 |
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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 semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This means that locally the leaves of F are fibres of a complex-valued harmonic morphism. In the Riemannian case, we prove that if the metric restricted to K is biinvariant then F is totally geodesic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15971 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Harmonic Morphisms on Lie groups and Minimal Conformal Foliations of Codimension two Gudmundsson, Sigmundur Munn, Thomas Jack Differential Geometry 53C35, 53C43, 58E20 Let G be a Lie group equipped with a left-invariant semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This means that locally the leaves of F are fibres of a complex-valued harmonic morphism. In the Riemannian case, we prove that if the metric restricted to K is biinvariant then F is totally geodesic. |
| title | Harmonic Morphisms on Lie groups and Minimal Conformal Foliations of Codimension two |
| topic | Differential Geometry 53C35, 53C43, 58E20 |
| url | https://arxiv.org/abs/2308.15971 |