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. In general 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. Spinning particles, such as Dirac fermions, can be described by pseudo-classical mechanics models involving anticommuting c-numbers for the spin-degrees of freedom. The configuration space of spinning particles (spinning space) is an extension of an ordinary Riemannian manifold, parametrized by local coordinates {xμ}, to a graded manifold parametrized by local coordinates {xμ, ψμ}, with the first set of variables being Grassmann-even ( commuting ) and the second set Grassmann-odd (anticommuting) [1-3]. The equation of motion of a spinning particle on a geodesic is derived from the action: S = ∫