Rigidity of the Stable Norm on Tori

given a closed, orientable riemannian manifold, we study the stable norm on the real homology groups. in particular, for n≥ 2 we prove that a riemannian n-torus, which has the same stable norms as a flat n-torus on the first and n-1 homology groups, is in fact isometric to the flat torus.