Abstract
This study provides a fundamental understanding of the geometry of a quasi-Sasakian manifold ( QS -manifold), highlighting their structural properties and enhancing the knowledge of their geometric framework. A pseudo quasi-conformal curvature tensor ( PQC -curvature tensor) of QS -manifold has been identified. The components of the PQC -curvature tensor are established employing the G -adjoined structure space( GADS -space). It is demonstrated that the Ricci flat QS -manifold is locally equivalent to the product of the complex Euclidean space Cn and the real line. Furthermore, it has been demonstrated that a ξ -pseudo quasi conformal flat QS -manifold is a quasi-Einstein manifold. The conditions under which a quasi-symmetric QS -manifold becomes a quasi-Einstein manifold are also specified. Subsequently, it has been shown for QS -manifolds that pseudo quasi conformal symmetric and pseudo quasi conformal flat are equivalent.•The pseudo quasi-conformal curvature tensor of the quasi Sasakian manifold has been identified.•The Ricci flat quasi Sasakian manifold is studied.•An application of the quasi-symmetric quasi Sasakian manifold to be a quasi-Einstein manifold is specified.