Malaysian Journal of Mathematical Sciences, June 2025, Vol. 19, No. 2
Pseudo-Quasi Conformal Curvature Tensor of Quasi Sasakian Manifold with Generalized Sasakian Space Forms
AlHusseini, F. H. and Abood, H. M.
Corresponding Email: habeeb.abood@uobasrah.edu.iq
Received date: 12 May 2024
Accepted date: 4 November 2024
Abstract:
The current study focuses on three main topics; the pseudo-quasi conformal curvature tensor, quasi-Sasakian manifolds ($ \mathcal{QSA}_{S}$-manifold), and generalized Sasakian space forms ($ \mathcal{GS}$-space forms) employing the $ \mathtt{G} $-adjoined structure space. For a $ \mathcal{QSA}_{S}$-manifold of $ \mathcal{GS}$-space forms, the components of the Ricci tensor and pseudo-quasi conformal curvature tensor are computed. Various types of $ \mathcal{QSA}_{S}$-manifold are described, and their interactions with $ \mathcal{GS}$-space forms are investigated. It has been shown that $ \xi $-pseudo quasi conformally flat $ \mathcal{QSA}_{S}$-manifold of $ \mathcal{GS}$-space forms includes quasi Einstein manifold. Furthermore, the condition of a quasi-pseudo quasi conformal $ \mathcal{QSA}_{S}$-manifold of space forms to be a quasi-Einstein manifold is identified. Finally, the scalar curvature is determined for $ \xi $-pseudo quasi-conformally flat $ \mathcal{QSA}_{S}$-manifold and quasi-pseudo quasi conformal $ \mathcal{QSA}_{S}$-manifold.
Keywords: quasi Sasakian manifold; generalized Sasakian space forms; pseudo-quasi conformal curvature tensor; quasi Einstein manifold
