Minimal Submanifolds of The Complex and Quaternionic Projective and Hyperbolic Spaces $\cn P^{2n-1}$, $\hn P^{n-1}$, $\cn H^{2n-1}$, $\hn H^{n-1}$ via Harmonic Morphisms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911662470070272 |
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| author | Gudmundsson, Sigmundur |
| author_facet | Gudmundsson, Sigmundur |
| contents | In this work we construct non-holomorphic, complete and minimal submanifolds of the odd-dimensional complex projective spaces $\cn P^{2n-1}$ and their dual complex hyperbolic spaces $\cn H^{2n-1}$. We then provide complete minimal submanifolds of the quaternionic projective spaces $\hn P^{n-1}$ and their dual quaternionic hyperbolic spaces $\hn H^{n-1}$. All the constructed minimal submanifolds are of codimension two. Our main tools are complex-valued harmonic morphisms from the above mentioned ambient spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal Submanifolds of The Complex and Quaternionic Projective and Hyperbolic Spaces $\cn P^{2n-1}$, $\hn P^{n-1}$, $\cn H^{2n-1}$, $\hn H^{n-1}$ via Harmonic Morphisms Gudmundsson, Sigmundur Differential Geometry 53C35, 53C43, 58E20 In this work we construct non-holomorphic, complete and minimal submanifolds of the odd-dimensional complex projective spaces $\cn P^{2n-1}$ and their dual complex hyperbolic spaces $\cn H^{2n-1}$. We then provide complete minimal submanifolds of the quaternionic projective spaces $\hn P^{n-1}$ and their dual quaternionic hyperbolic spaces $\hn H^{n-1}$. All the constructed minimal submanifolds are of codimension two. Our main tools are complex-valued harmonic morphisms from the above mentioned ambient spaces. |
| title | Minimal Submanifolds of The Complex and Quaternionic Projective and Hyperbolic Spaces $\cn P^{2n-1}$, $\hn P^{n-1}$, $\cn H^{2n-1}$, $\hn H^{n-1}$ via Harmonic Morphisms |
| topic | Differential Geometry 53C35, 53C43, 58E20 |
| url | https://arxiv.org/abs/2605.03651 |