Space-Times Admitting Killing-Yano Tensors. II

In this paper we derive canonical line elements admitting a simple Killing-Yano tensor f^*_ab. There exist three distinct cases according to the character of f^*_ab (spacelike, timelike, null). We reveal several close analogies between the vector field l^a = f^*a_rp^r along a geodesic with tangent field p^r and the angular momentum l = r x p in the case of a spacelike Killing-Yano tensor. In particular, we show that, in consequence of the Killing-Yano tensor equations, there exists an analogue of the three-dimensional position vector field in certain hypersurfaces and that l^a can be written in the form (r x p)^a. Furthermore, an analogue of the 'equatorial plane' of the classical Kepler problem can be constructed intrinsically.