Quasi Sasakian manifold endowed with vanishing pseudo quasi conformal curvature tensor

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