Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime

In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal eta-Ricci soliton with torse-forming vector field xi. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed. of the soliton is of gradient type, we derive, from the conformal eta-Ricci soliton equation, a Laplacian equation.