Moduli of triples of points in quaternionic hyperbolic geometry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914636188614656 |
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| author | Almeida, Igor Gusevskii, Nikolay |
| author_facet | Almeida, Igor Gusevskii, Nikolay |
| contents | In this work, we describe the moduli of triples of points in quaternionic projective space which define uniquely the congruence classes of such triples relative to the action of the isometry group of quaternionic hyperbolic space ${\rm H}^n_{\mathbb{Q}}$. To solve this problem, we introduce some basic invariants of triples of points in quaternionic hyperbolic geometry. In particular, we define quaternionic analogues of the Goldman invariants for mixed configurations of points introduced by him in complex hyperbolic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00745 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moduli of triples of points in quaternionic hyperbolic geometry Almeida, Igor Gusevskii, Nikolay Differential Geometry 32H20, 20H10, 22E40, 57S30, 32G07, 32C16 In this work, we describe the moduli of triples of points in quaternionic projective space which define uniquely the congruence classes of such triples relative to the action of the isometry group of quaternionic hyperbolic space ${\rm H}^n_{\mathbb{Q}}$. To solve this problem, we introduce some basic invariants of triples of points in quaternionic hyperbolic geometry. In particular, we define quaternionic analogues of the Goldman invariants for mixed configurations of points introduced by him in complex hyperbolic geometry. |
| title | Moduli of triples of points in quaternionic hyperbolic geometry |
| topic | Differential Geometry 32H20, 20H10, 22E40, 57S30, 32G07, 32C16 |
| url | https://arxiv.org/abs/2301.00745 |