On the geometry of LP-Sasakian manifolds associated with the extended quasi-conformal curvature tensor

Abstract

The geometry of LP-Sasakian manifolds and their interaction with various curvature tensors—particularly conformal, quasi-conformal, and concircular tensors—has been extensively studied in the literature. However, most existing works focus on classical curvature tensors or standard quasi-conformal curvature structures under general or well-known curvature restrictions. The present study introduces and investigates an extended quasi-conformal curvature tensor, which generalizes the traditional quasi-conformal curvature tensor by incorporating additional structural components adapted to LP-Sasakian manifolds.
In particular, we focus on LP-Sasakian manifolds with in the frame work of the extended quasi-conformal curvature tensor satisfying the vanishing conditions $K_{e}(U_{1},Y_{1})Z_{1}=0$ and $(R(\xi,Y_{1})\cdot K_{e})(U_{1},V_{1})W_{1}=0$. Furthermore, the existence and properties of Ricci soliton structures are also examined.