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 $n\geq 2$ 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.
- Autores:
-
Osuna, Osvaldo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2010
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/39796
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/39796
http://bdigital.unal.edu.co/29893/
- Palabra clave:
- Stable norm
$p$-norm
Poincaré duality
53C23
53D25
53C24
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Given a closed, orientable Riemannian manifold, we study the stable norm on the real homology groups. In particular, for $n\geq 2$ 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. |
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