Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs spacetimes

Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs spacetimes are classified according to their Ricci collineation vector (RCV) field of the form (I)-(iv) one component of xi (a)(x(b)) is nonzero, (v)-(x) two components of xi (a)(x(b)) are nonzero, and (xi)-(xiv) three components of xi (a)(x(b)) are nonzero. Their relation with isometries of the spacetimes 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.