The aim of the present paper is to study Ricci soliton, η-Ricci soliton and various types of curvature tensors on Generalized Sasakian space form. We have also studied conformal Killing vector field, torse forming vector field on Generalized Sasakian space form. We have also established suitable examples of kenmotsu manifold, Sasakian manifold and cosymplectic manifold respectively.

We carry out geometric attribution of perfect fluid space-time in terms of a Riemann soliton with a torse forming vector field. It is shown that a perfect fluid space-time becomes a dark fluid space-time when we represent the timelike velocity vector field to be a torse-forming vector field. Next, we have investigated the nature of a Riemann soliton in perfect fluid space-time under certain curvature conditions in terms of the cosmological constant, the gravitational constant, energy density and isotropic pressure. We have also constructed an example of Riemann soliton in perfect fluid space-time. Finally, we have classified the Riemann soliton in a perfect fluid space-time obeying \(f(r,T)\)-gravity in terms of energy density and isotropic pressure.