  Let X be a complex Fano-manifolds with second Betti-number 1 which carries a
contact structure. It follows from previous work that such a manifold can
always be covered by lines. Thus, it seems natural to consider the geometry of
lines in greater detail.
  In this brief note we show that if x in X is a general point, then all lines
through x are smooth. If X is not the projective space, then the tangent spaces
to lines generate the contact distribution at x. As a consequence we obtain
that the contact structure on X is unique, a result previously obtained by C.
LeBrun in the case that X is a twistor space.
