Geometry of paraquaternionic contact structures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866914780369911808 |
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| author | Tchomakova, Marina Ivanov, Stefan Zamkovoy, Simeon |
| author_facet | Tchomakova, Marina Ivanov, Stefan Zamkovoy, Simeon |
| contents | We introduce the notion of paraquaternionic contact structures (pqc structures), which turns out to be a generalization of the para 3-Sasakian geometry. We derive a distinguished linear connection preserving the pqc structure. Its torsion tensor is expressed explicitly in terms of the structure tensors and the structure equations of a pqc manifold are presented. We define pqc-Einstein manifolds and show that para 3-Sasakian spaces are precisely pqc manifolds, which are pqc-Einstein. Furthermore, we introduce the paraquaternionic Heisenberg qroup and show that it is the flat model of the pqc geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of paraquaternionic contact structures Tchomakova, Marina Ivanov, Stefan Zamkovoy, Simeon Differential Geometry High Energy Physics - Theory We introduce the notion of paraquaternionic contact structures (pqc structures), which turns out to be a generalization of the para 3-Sasakian geometry. We derive a distinguished linear connection preserving the pqc structure. Its torsion tensor is expressed explicitly in terms of the structure tensors and the structure equations of a pqc manifold are presented. We define pqc-Einstein manifolds and show that para 3-Sasakian spaces are precisely pqc manifolds, which are pqc-Einstein. Furthermore, we introduce the paraquaternionic Heisenberg qroup and show that it is the flat model of the pqc geometry. |
| title | Geometry of paraquaternionic contact structures |
| topic | Differential Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.16713 |