Remark on quasi Sasakian structures

Emmanuel Gnandi; Fortuné Massamba

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arXiv · 2512.21378

Remark on quasi Sasakian structures

Emmanuel Gnandi·Fortuné Massamba

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Abstract

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 K\"ahler mapping torus. In particular, every quasi-Sasakian structure in this setting can be deformed into a Sasakian or a co-K\"ahler 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.

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Emmanuel Gnandi, Fortuné Massamba. 2025-12-24. Remark on quasi Sasakian structures. https://arxiv.org/abs/2512.21378

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