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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1911.06120 |
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| _version_ | 1866913261224460288 |
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| author | Gentili, Graziano Gori, Anna Sarfatti, Giulia |
| author_facet | Gentili, Graziano Gori, Anna Sarfatti, Giulia |
| contents | This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that on an affine quaternionic manifold there is one and only one affine quaternionic structure. A direct result, based on the celebrated Kodaira Theorem that studies compact complex manifolds in complex dimension 2, states that the only compact affine quaternionic curves are the quaternionic tori and the primary Hopf surface S^3 x S^1. As for compact affine quaternionic surfaces, we restrict to the complete ones: the study of their fundamental groups, together with the inspection of all nilpotent hypercomplex simply connected 8-dimensional Lie Groups, identifies a path towards their classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_06120 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On compact affine quaternionic curves and surfaces Gentili, Graziano Gori, Anna Sarfatti, Giulia Differential Geometry Complex Variables 30G35, 53C15 This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that on an affine quaternionic manifold there is one and only one affine quaternionic structure. A direct result, based on the celebrated Kodaira Theorem that studies compact complex manifolds in complex dimension 2, states that the only compact affine quaternionic curves are the quaternionic tori and the primary Hopf surface S^3 x S^1. As for compact affine quaternionic surfaces, we restrict to the complete ones: the study of their fundamental groups, together with the inspection of all nilpotent hypercomplex simply connected 8-dimensional Lie Groups, identifies a path towards their classification. |
| title | On compact affine quaternionic curves and surfaces |
| topic | Differential Geometry Complex Variables 30G35, 53C15 |
| url | https://arxiv.org/abs/1911.06120 |