In this paper, we have examined charged strange quark matter attached to the string cloud in the spherical symmetric space-time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for spherical symmetric space-time with strange quark matter attached to the string cloud via conformal motions. Also, we have discussed the features of the obtained solutions.

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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 ξ a (x b ) is different from zero and (ii) two components of ξ a (x b ) are different from zero, for a, b = 1, 2, 3, 4, are presented. In subcase (i.b), which is ξ a = (0, ξ 2 (x a ), 0, 0), some known solutions are found, and in subcase (i.d), which is ξ a = (0, 0, 0, ξ 4 (x a )), choosing S(t) = const.×R(t), the Bianchi type II, VIII, and IX spacetimes is reduced to the Robertson-Walker metric.

Ricci collineations of the Bianchi types I and III, and KantowskiSachs space-times are classified according to their Ricci collineation vector (RCV) field of the form (i)-(iv) one component of ξ a (x b ) is nonzero, (v)-(x) two components of ξ a (x b ) are nonzero, and (xi)-(xiv) three components of ξ a (x b ) are nonzero. Their relation with isometries of the space-times is established. In case (v), when det(R ab ) = 0, some metrics are found under the time transformation, in which some of these metrics are known, and the other ones new. Finally, the family of contracted Ricci collineations (CRC) are presented.

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