$(\alpha,\beta)$-Type almost $\eta$-Ricci-Yamabe solitons in perfect fluid spacetime

Abstract

In this paper, we consider perfect fluid spacetime admitting $(\alpha,\beta)$-type almost $\eta$-Ricci--Yamabe solitons by means of some curvature tensors. Ricci pseudosymmetry concepts of perfect fluid spacetime  admitting $(\alpha,\beta)$-type almost $\eta$-Ricci--Yamabe soliton are introduced according to the choice of some special curvature tensors such as Riemann, concircular and projective curvature tensor. After then,  according to choosing of the curvature tensors, necessary conditions are given for perfect fluid spacetime admitting $(\alpha,\beta)$-type almost $\eta$-Ricci--Yamabe soliton to be Ricci semisymmetric. Then, some important characterizations are given for Ricci, Yamabe, Einstein and $\eta$-Einstein solitons on perfect fluid spacetime.