Abstract

OSUNA, OSVALDO. Rigidity of the Stable Norm on Tori. Rev.colomb.mat. [online]. 2010, vol.44, n.1, pp. 15-21. ISSN 0034-7426.

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.

Keywords : Stable norm; p-norm; Poincaré duality.