Space—times admitting Killing—Yano tensors. II

Abstract
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$^{*a}_r$p$^r$ 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.

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