Remark on quasi Sasakian structures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908731674984448 |
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| author | Gnandi, Emmanuel Massamba, Fortuné |
| author_facet | Gnandi, Emmanuel Massamba, Fortuné |
| contents | In this work, we revisit quasi-Sasakian geometry in dimension three and examine how these structures interact with the foliation generated by the Reeb vector field and its basic cohomology. Through a deformation-based approach, we show that a closed, orientable $3$-manifold admits a quasi-Sasakian structure precisely when it is either Sasakian or arises as a Kähler mapping torus. In particular, every quasi-Sasakian structure in this setting can be deformed into a Sasakian or a co-Kähler one. This result leads to a complete classification of quasi-Sasakian manifolds in dimension three and highlights the geometric and topological features that distinguish the two cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remark on quasi Sasakian structures Gnandi, Emmanuel Massamba, Fortuné Differential Geometry 53C25, 53D15 In this work, we revisit quasi-Sasakian geometry in dimension three and examine how these structures interact with the foliation generated by the Reeb vector field and its basic cohomology. Through a deformation-based approach, we show that a closed, orientable $3$-manifold admits a quasi-Sasakian structure precisely when it is either Sasakian or arises as a Kähler mapping torus. In particular, every quasi-Sasakian structure in this setting can be deformed into a Sasakian or a co-Kähler one. This result leads to a complete classification of quasi-Sasakian manifolds in dimension three and highlights the geometric and topological features that distinguish the two cases. |
| title | Remark on quasi Sasakian structures |
| topic | Differential Geometry 53C25, 53D15 |
| url | https://arxiv.org/abs/2512.21378 |