Space—times admitting Killing—Yano tensors. II

Abstract

In this paper we derive canonical line elements admitting a simple KillingYano tensor f* ab. There exist three distinct cases according to the character o f f* ab (spacelike, timelike, null). We reveal several close analogies between the vector field la = f * arp r along a geodesic with tangent field p r and the angular momentum l = rxpin 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 th at la 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.