Structural equations for a special class of conformal killing tensors of arbitrary valence

A symmetric tensor T on a (pseudo-)Riemannian manifold which satisfies Ti1,i2,…|j=S(i1,i2,…,ir−1gir)j for some symmetric tensor S is a conformai Killing tensor of a special kind. Such special conformai Killing tensors of valence 1 and 2 have been extensively studied. In this paper special conformai Killing tensors of arbitrary valence, and indeed certain non-metrical generalizations of them, are investigated. In particular, it is shown that the space of special conformai Killing tensors is finite dimensional, and the maximal dimension is attained (in the (pseudo-)Riemannian case) if and only if the manifold is a space of constant curvature. This result is obtained by constructing a set of structural equations for special conformai Killing tensors.