N(k)N(k)-quasi Einstein manifolds satisfying certain conditions

We consider N(k)N(k)-quasi Einstein manifolds satisfying the conditions R(ξ,X)·P=0,P(ξ,X)·S=0R(ξ,X)·P=0,P(ξ,X)·S=0 and P(ξ,X)·P=0P(ξ,X)·P=0. We construct physical examples of N(k)N(k)-quasi Einstein space–times.