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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. v.44 n.1 Bogotá jan./jun. 2010

 

Rigidity of the Stable Norm on Tori

Rigidez de la norma estable sobre toros

OSVALDO OSUNA1

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


Abstract

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.


2000 Mathematics Subject Classification: 53C23, 53D25, 53C24.

Resumen

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.


Texto completo disponible en PDF


References

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(Recibido en julio de 2008. Aceptado en abril de 2010)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv44n1a02,
    AUTHOR  = {Osuna, Osvaldo},
    TITLE   = {{Rigidity of the Stable Norm on Tori}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2010},
    volume  = {44},
    number  = {1},
    pages   = {15-21}
}

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