Abstract
Much attention has been paid to the (Euclidean) Taub-NUT metric because the geodesic on this space describes approximately the motion of two well-separated interacting monopoles. It is also well known that the Taub-NUT metric admits a Kepler-type symmetry. In this paper, the Taub-NUT metric is extended so that it still admits a Kepler-type symmetry. The geodesics of this metric will be investigated. In particular, regularization of singular geodesics is studied by use of a method from dynamical systems. Further, some geometrical properties of the extended Taub-NUT metric are cleared up. In order that the extended Taub-NUT metric either has a self-dual Riemann curvature tensor or is an Einstein metric, it is necessary and sufficient that it coincides with the original Taub-NUT metric up to a constant factor. Furthermore, a class of extended Taub-NUT metrics have a self-dual Weyl curvature tensor is found. This class of metrics, of course, includes the Taub-NUT metric.
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