Space–times admitting Killing–Yano tensors. I

This is the first of two papers dealing with Killing–Yano tensors. In this paper, Killing–Yano tensors are classified according to their valence. The cases of valence 1, 3 and 4 are trivial or almost trivial. Canonical line elements of metrics admitting Killing–Yano tensors of valence 2 and rank 4 are derived without any further restrictions. (The case of rank 2 will be treated in part II of this series.) Furthermore, we give a relativistic analogy of the classical Kepler motion in a plane if there is no force com­ponent orthogonal to this plane. This analogy demonstrates the way in which a Killing–Yano tensor may be considered as being related to the angular momentum of a particle.