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.

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  The pseudo quasi-conformal curvature tensor of the quasi Sasakian manifold has been identified.
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  The Ricci flat quasi Sasakian manifold is$$studied.
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  An application of the quasi-symmetric quasi Sasakian manifold to be a quasi-Einstein manifold is specified.