Ricci collineations of the Bianchi type II,VIII, and IX space-times

Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX space-times, associated with the vector fields of the form (i) one component of ^a (x ^b ) is different from zero and (ii) two components of ^a (x ^b ) are different from zero, fora, b=1, 2, 3, 4, are presented. In subcase (i.b), which is ^a = (0, ¹(x ^a ),0,0), some known solutions are found, and in subcase (i.d), which is ^a =(0, 0, 0, ⁴(x ^a )), choosingS(t) = const.×R(t), the Bianchi type II, VIII, and IX spacetime is reduced to the Robertson-Walker metric.