  The Levi-Civita connection and geodesic equations for a stationary spacetime
are studied in depth. General formulae which generalize those for warped
products are obtained. These results are applicated to some regions of Kerr
spacetime previously studied by using variational methods. We show that they
are neither space-convex nor geodesically connected. Moreover, the whole
stationary part of Kerr spacetime is not geodesically connected, except when
the angular momentum is equal to zero (Schwarzschild spacetime).
