  A riemannian manifold is secure if the geodesics between any pair of points
in the manifold can be blocked by a finite number of point obstacles. Compact,
flat manifolds are secure. A standing conjecture says that these are the only
secure, compact riemannian manifolds. The conjecture claims, in particular,
that a riemannian torus of any dimension is secure if and only if it is flat.
We prove this for two-dimensional tori.
