Generalized Killing equations for spinning spaces and the role of Killing-Yano tensors

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. The constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables. The general results are applied to the case of the four-dimensional Euclidean Taub-NUT spinning space.