A Study of a Riemann Soliton in a Perfect Fluid Space-Time and $$\boldsymbol{f(r,T)}$$-Gravity

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.