Geodesics on metrics of self-dual Taub-Nut type
Geodesic equations are solved when at least two of $τ$, $θ$, $φ$ are constant on metrics of self-dual Taub-NUT type. They can also be solved also on self-dual Taub-NUT metrics if only $r$, $θ$ or $φ$ is constant. However, the explicit solution of the geodesic equations is not available yet if only $τ$ is constant.
math.DG↗