Hyper generalized quasi-Einstein manifolds and their applications

Abstract

The object of the present paper is to study hyper generalized quasi-Einstein (HGQE) manifolds, focusing on their geometric and physical contributions. Among others things, it establishes that conhar monically flat Ricci semisymmetric HGQE manifolds enforce co-directionality among generators. Further, we prove that if the timelike vector field is a torse-forming vector field, then a HGQE spacetime with a Ricci soliton is a perfect fluid spacetime. We also show that a HGQE spacetime obeying Einstein’s field equation with an energy-momentum tensor fulfilling the Codazzi condition is a Yang pure space. Ultimately, we construct an example to demonstrate the existence of HGQE spacetime.