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
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Osuna, Osvaldo1393564f-d7b8-45e5-b7f7-9267bc186d1e3002019-06-28T04:28:00Z2019-06-28T04:28:00Z2010https://repositorio.unal.edu.co/handle/unal/39796http://bdigital.unal.edu.co/29893/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.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/28589Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 44, núm. 1 (2010); 15-21 0034-7426Osuna, Osvaldo (2010) Rigidity of the stable norm on tori. Revista Colombiana de Matemáticas; Vol. 44, núm. 1 (2010); 15-21 0034-7426 .Rigidity of the stable norm on toriArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTStable norm$p$-normPoincaré duality53C2353D2553C24ORIGINAL28589-142424-1-PB.htmltext/html5115https://repositorio.unal.edu.co/bitstream/unal/39796/1/28589-142424-1-PB.html1471c33d1572f758e5891660f7486997MD5128589-102373-1-PB.pdfapplication/pdf149331https://repositorio.unal.edu.co/bitstream/unal/39796/2/28589-102373-1-PB.pdf3aa0440bc5b69a6fcbc745e45b8aa500MD52THUMBNAIL28589-102373-1-PB.pdf.jpg28589-102373-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg4617https://repositorio.unal.edu.co/bitstream/unal/39796/3/28589-102373-1-PB.pdf.jpg6dab1b0e8409301a5e757f44a85b3cc6MD53unal/39796oai:repositorio.unal.edu.co:unal/397962024-01-21 23:06:47.608Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Rigidity of the stable norm on tori
title Rigidity of the stable norm on tori
spellingShingle Rigidity of the stable norm on tori
Stable norm
$p$-norm
Poincaré duality
53C23
53D25
53C24
title_short Rigidity of the stable norm on tori
title_full Rigidity of the stable norm on tori
title_fullStr Rigidity of the stable norm on tori
title_full_unstemmed Rigidity of the stable norm on tori
title_sort Rigidity of the stable norm on tori
dc.creator.fl_str_mv Osuna, Osvaldo
dc.contributor.author.spa.fl_str_mv Osuna, Osvaldo
dc.subject.proposal.spa.fl_str_mv Stable norm
$p$-norm
Poincaré duality
53C23
53D25
53C24
topic Stable norm
$p$-norm
Poincaré duality
53C23
53D25
53C24
description 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.
publishDate 2010
dc.date.issued.spa.fl_str_mv 2010
dc.date.accessioned.spa.fl_str_mv 2019-06-28T04:28:00Z
dc.date.available.spa.fl_str_mv 2019-06-28T04:28:00Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/39796
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/29893/
url https://repositorio.unal.edu.co/handle/unal/39796
http://bdigital.unal.edu.co/29893/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/28589
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 44, núm. 1 (2010); 15-21 0034-7426
dc.relation.references.spa.fl_str_mv Osuna, Osvaldo (2010) Rigidity of the stable norm on tori. Revista Colombiana de Matemáticas; Vol. 44, núm. 1 (2010); 15-21 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
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dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
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