  In connection with the study of shear-free null geodesics in Minkowski space,
we investigate the real geometric effects in real Minkowski space that are
induced by and associated with complex world-lines in complex Minkowski space.
It was already known, in a formal manner, that complex analytic curves in
complex Minkowski space induce shear-free null geodesic congruences. Here we
look at the direct geometric connections of the complex line and the real
structures. Among other items, we show, in particular, how a complex world-line
projects into the real Minkowski space in the form of a real shear-free null
geodesic congruence.
