SOLITONS AND GEOMETRICAL STRUCTURES IN A PERFECT FLUID SPACETIME

Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and eta-Ricci and eta-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector field xi of the soliton is of gradient type, xi := grad( f), we derive a Poisson equation from the soliton equation.