GEOMETRICAL PROPERTIES OF GENERALIZED QUASI-CONFORMAL CURVATURE TENSOR

This paper examines the generalized quasi-conformal curvature $\mathcal{G}$, which generalizes the concept of conformal curvature tensor $\mathcal{C}$, quasi-conformal curvature tensor $\mathcal{\widetilde{C}}$, projective curvature tensor $\mathcal{P}$, pseudo projective curvature tensor $\mathcal{\widetilde{P}}$, and pseudo $W_2-$curvature tensor $\mathcal{\widetilde{W}}_2$. Initially, we acquire some geometrical features. Subsequently, we examine pseudo generalized conformal symmetric manifolds. Divergence-free generalized quasi-conformal curvature tensor is derived from the Gray's decomposition. Additionally, we also examine Einstein $(P\mathcal{G}S)_n$ manifolds. A study of generalized quasi-conformal has been conducted as the four-dimensional spacetime of general relativity $\widetilde{GR}$. Ultimately, we examine a non-trivial Lorentzian metric of $(P\mathcal{G}S)_4$.