  Given a closed Riemannian manifold (M, g), there is a partition \Sigma_i of
its tangent bundle TM called the focal decomposition. The sets \Sigma_i are
closely associated to focusing of geodesics of (M, g), i.e. to the situation
where there are exactly i geodesic arcs of the same length joining points p and
q in M. In this note, we study the topological structure of the focal
decomposition of a closed Riemannian manifold and its relation with the metric
structure of the manifold. Our main result is that the flat n-tori are focally
rigid, in the sense that if two flat tori are focally equivalent, then the tori
are isometric up to rescaling.
