An almost contact metric structure on a differentiable manifold \(\widetilde {M}\) is a quasi-Sasakian structure if it is normal and its fundamental 2-form is closed. A manifold with a quasi-Sasakian structure is called quasi-Sasakian manifold. D. E. Blair introduced in Blair (J Differ Geom 1:331–345, 1967) the notion of quasi-Sasakian manifold to unify the concepts of Sasakian and cosymplectic manifolds. Geometry of quasi-Sasakian manifolds has become the subject of much interest as it has significant importance and applications in physics and, in particular, magnetic theory and supergravity.