¹Universidad Michoacana, Morelia, México. Email: osvaldo@ifm.umich.mx

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.

Key words: Stable norm, p-norm, Poincaré duality.

Dada una variedad Riemanniana, cerrada y orientable, estudiamos la norma estable sobre sus grupos de homología real. En particular, para n≥ 2 demostramos que si un n-toro Riemanniano tiene normas estables iguales a las normas estables de un n-toro plano sobre el primer y n-1 grupos de homología; entonces es isométrico a dicho toro plano.

Palabras clave: Norma estable, p-norma, dualidad de Poincaré.

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