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<p>In this work, we revisit quasi-Sasakian structures 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.</p>

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Remarks on quasi-Sasakian structures

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Emmanuel Gnandi,
  • Fortuné Massamba

摘要

In this work, we revisit quasi-Sasakian structures 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.