Conformal Killing tensors in reducible spaces

It is shown that the dimension of the vector space of second order, trace-free conformal Killing tensors (CKT’s) in a Riemannian space of dimension n (?3) is bounded above by (1/12)(n−1)(n+2)(n+3)(n+4) and that this is attained in flat space. The discussion is eventually restricted to four-dimensional spaces which admit a two-dimensional, Abelian, orthogonally transitive symmetry group, as well as one nonredundant CKT. A sufficient condition is given for an empty space to be Type D.