  We give a necessary condition on a geodesic in a Riemannian manifold that can
run in some convex hypersurface. As a corollary we obtain peculiar properties
that hold true for every convex set in any generic Riemannian manifold (M,g).
For example, if a convex set in (M,g) is bounded by a smooth hypersurface, then
it is strictly convex.
