RICCI COLLINEATIONS OF THE BIANCHI TYPE-II, TYPE-VIII, AND TYPE-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 xi(alpha)(x(b)) is different from zero and (ii) two components of xi(alpha)(x(b)) are different from zero, for a, b = 1, 2 , 3, 4, are presented. In subcase (i.b), which is xi(alpha) = (0, xi(1 )(x(alpha)), 0, 0), some known solutions are found, and in subcase (i. d), which is xi(alpha) = (0, 0, 0, xi(4)(x(alpha))) choosing S(t) = co nst. x R(t), the Bianchi type II, VIII, and IX spacetime is reduced to the Robertson-Walker metric.