Abstract

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 $(P\mathcal{G}S)_4$.

Keywords and Phrases

Pseudo symmetric, perfect fluid, Einstein's field equation, Quasi-conformal curvature tensor $\mathcal{\widetilde{C}}$, pseudo projective curvature tensor $\mathcal{\widetilde{P}}$, conformal curvature tensor $\mathcal{ C }$, projective curvature tensor $\mathcal{ P }$, concircular curvature tensor $\mathcal{ L }$, generalized quasi conformal curvature tensor $\mathcal{ G }$, Gray's decomposition.

A.M.S. subject classification

53C25, 53D15.

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