Generalized Killing tensors

Generalized Killing tensors are defined and the integrability conditions di scussed to show that the familiar result that a space of constant curvature admits the maximum number of Killing vectors and second order Killing tens ors does not necessarily generalize. The existence of second order Generali zed Killing Yano tensors in spherically symmetric static space-times is inv estigated and a non-redundant example is given. Ir is proved that the natur al vector analogue of the Lenz-Runge vector does not exist.