  We have developed a general geometric treatment of the GCE valid for any
stationary axisymmetric metric. The method is based on the remark that the
world lines of objects rotating along spacely circular trajectories are in any
case, for those kind of metrics, helices drawn on the flat bidimensional
surface of a cylinder. Applying the obtained formulas to the special cases of
the Kerr and weak field metric for a spinning body, known results for time
delays and synchrony defects are recovered.
