  Complex contact manifolds have recently received considerable attention. Many
of the newer publications approach contact manifolds via the covering family of
minimal rational curves. This short note furthers the study of these curves.
  It is known that for any point x in X, the subvariety, which is covered by
those curves which contain x, is Legendrian. We will now study the deformations
of these subvarieties which are generated by moving the base point.
  As a main application, we give a positive answer to a question of J.M. Hwang
in the case of contact manifolds: a sufficiently general tangent vector is
contained in at most a single minimal rational curve. The author believes that
this is a necessary step towards a full classification of contact manifolds.
  We give a second application by showing that the normalization of the
subvariety of minimal curves through x is isomorphic to a projective cone.
