for all vector fields X, Y where S is the Ricci tensor of the type (0, 2), r is the scalar curvature, k is the gravitational constant and T is the energy momentum tensor of type (0, 2).

The energy momentum tensor T is said to describe a perfect fluid [2] if

In a Lorentzian para- Sasakian type spacetime by considering the characteristic vector field [xi] as the flow vector field of the fluid, the energy momentum tensor takes the form

Although there are physical arguments for equating the Einstein tensor to the

energy momentum tensor ([G.

In the general theory of relativity, energy momentum tensor plays an important role and the condition on energy momentum tensor for a perfect fluid space time changes the nature of space time (5).

We know an energy momentum tensor T will be covariant recurrent (6) if

So we like to define generalized covariant recurrent energy momentum tensor as follows:

An energy momentum tensor T is said to be generalized covariant recurrent if

Generalized recurrent energy momentum tensor in a general relativistic space time

ij] being the ordinary

energy momentum tensor associated to isotropic matter and radiation.

where k is the Einstein's gravitational constant, T is the

energy momentum tensor of type (0,2) given by

The

energy momentum tensor in this symmetry (and this particular case) is: