New Minimal Surfaces of the Sphere $S^4$ and the Hyperbolic Space $H^4$ via Harmonic Morphisms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914421074296832 |
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| author | Gudmundsson, Sigmundur Löhndorf, Leonard Nygren |
| author_facet | Gudmundsson, Sigmundur Löhndorf, Leonard Nygren |
| contents | In this work we introduce a new method for the construction of minimal submanifolds of codimension two in even dimensional spheres and hyperbolic spaces. This is based on the theory of complex-valued harmonic morphisms. This gives the first explicit examples of such maps defined on the sphere $S^4$ and the hyperbolic space $H^4$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New Minimal Surfaces of the Sphere $S^4$ and the Hyperbolic Space $H^4$ via Harmonic Morphisms Gudmundsson, Sigmundur Löhndorf, Leonard Nygren Differential Geometry 53C35, 53C43, 58E20 In this work we introduce a new method for the construction of minimal submanifolds of codimension two in even dimensional spheres and hyperbolic spaces. This is based on the theory of complex-valued harmonic morphisms. This gives the first explicit examples of such maps defined on the sphere $S^4$ and the hyperbolic space $H^4$. |
| title | New Minimal Surfaces of the Sphere $S^4$ and the Hyperbolic Space $H^4$ via Harmonic Morphisms |
| topic | Differential Geometry 53C35, 53C43, 58E20 |
| url | https://arxiv.org/abs/2603.24301 |