Manifolds of semi-negative curvature
- Autores
- Conde, Cristian Marcelo; Larotonda, Gabriel Andrés
- Año de publicación
- 2010
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- This paper studies the metric structure of manifolds of semi-negative curvature. Explicit estimates on the geodesic distance and sectional curvature are obtained in the setting of homogeneous spaces G/K of Banach–Lie groups, and a characterization of convex homogeneous submanifolds is given in terms of the Banach–Lie algebras. A splitting theorem via convex expansive submanifolds is proved, inducing the corresponding splitting of the Banach–Lie group G. The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces, and manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class of nonpositively curved spaces. Several well-known results, such as the existence and uniqueness of best approximations from convex closed sets, or the Bruhat–Tits fixed-point theorem, are shown to hold in this setting, without dimension restrictions. Finally, these notions are used to study the structure of the classical Banach–Lie groups of bounded linear operators acting on a Hilbert space, and the splittings induced by conditional expectations in such a setting.
Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina - Materia
-
Homogeneous Manifold
Nonpositive Curvature
Positive Operator
Short Geodesic - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19426
Ver los metadatos del registro completo
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Manifolds of semi-negative curvatureConde, Cristian MarceloLarotonda, Gabriel AndrésHomogeneous ManifoldNonpositive CurvaturePositive OperatorShort Geodesichttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper studies the metric structure of manifolds of semi-negative curvature. Explicit estimates on the geodesic distance and sectional curvature are obtained in the setting of homogeneous spaces G/K of Banach–Lie groups, and a characterization of convex homogeneous submanifolds is given in terms of the Banach–Lie algebras. A splitting theorem via convex expansive submanifolds is proved, inducing the corresponding splitting of the Banach–Lie group G. The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces, and manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class of nonpositively curved spaces. Several well-known results, such as the existence and uniqueness of best approximations from convex closed sets, or the Bruhat–Tits fixed-point theorem, are shown to hold in this setting, without dimension restrictions. Finally, these notions are used to study the structure of the classical Banach–Lie groups of bounded linear operators acting on a Hilbert space, and the splittings induced by conditional expectations in such a setting.Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaWiley2010-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19426Conde, Cristian Marcelo; Larotonda, Gabriel Andrés; Manifolds of semi-negative curvature; Wiley; Proceedings Of The London Mathematical Society; 100; 3; 4-2010; 670-7040024-6115CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/plms/pdp042/abstractinfo:eu-repo/semantics/altIdentifier/doi/10.1112/plms/pdp042info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:28:56Zoai:ri.conicet.gov.ar:11336/19426instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:28:56.932CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Manifolds of semi-negative curvature |
title |
Manifolds of semi-negative curvature |
spellingShingle |
Manifolds of semi-negative curvature Conde, Cristian Marcelo Homogeneous Manifold Nonpositive Curvature Positive Operator Short Geodesic |
title_short |
Manifolds of semi-negative curvature |
title_full |
Manifolds of semi-negative curvature |
title_fullStr |
Manifolds of semi-negative curvature |
title_full_unstemmed |
Manifolds of semi-negative curvature |
title_sort |
Manifolds of semi-negative curvature |
dc.creator.none.fl_str_mv |
Conde, Cristian Marcelo Larotonda, Gabriel Andrés |
author |
Conde, Cristian Marcelo |
author_facet |
Conde, Cristian Marcelo Larotonda, Gabriel Andrés |
author_role |
author |
author2 |
Larotonda, Gabriel Andrés |
author2_role |
author |
dc.subject.none.fl_str_mv |
Homogeneous Manifold Nonpositive Curvature Positive Operator Short Geodesic |
topic |
Homogeneous Manifold Nonpositive Curvature Positive Operator Short Geodesic |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
This paper studies the metric structure of manifolds of semi-negative curvature. Explicit estimates on the geodesic distance and sectional curvature are obtained in the setting of homogeneous spaces G/K of Banach–Lie groups, and a characterization of convex homogeneous submanifolds is given in terms of the Banach–Lie algebras. A splitting theorem via convex expansive submanifolds is proved, inducing the corresponding splitting of the Banach–Lie group G. The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces, and manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class of nonpositively curved spaces. Several well-known results, such as the existence and uniqueness of best approximations from convex closed sets, or the Bruhat–Tits fixed-point theorem, are shown to hold in this setting, without dimension restrictions. Finally, these notions are used to study the structure of the classical Banach–Lie groups of bounded linear operators acting on a Hilbert space, and the splittings induced by conditional expectations in such a setting. Fil: Conde, Cristian Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina |
description |
This paper studies the metric structure of manifolds of semi-negative curvature. Explicit estimates on the geodesic distance and sectional curvature are obtained in the setting of homogeneous spaces G/K of Banach–Lie groups, and a characterization of convex homogeneous submanifolds is given in terms of the Banach–Lie algebras. A splitting theorem via convex expansive submanifolds is proved, inducing the corresponding splitting of the Banach–Lie group G. The notion of nonpositive curvature in Alexandrov's sense is extended to include p-uniformly convex Banach spaces, and manifolds of semi-negative curvature with a p-uniformly convex tangent norm fall in this class of nonpositively curved spaces. Several well-known results, such as the existence and uniqueness of best approximations from convex closed sets, or the Bruhat–Tits fixed-point theorem, are shown to hold in this setting, without dimension restrictions. Finally, these notions are used to study the structure of the classical Banach–Lie groups of bounded linear operators acting on a Hilbert space, and the splittings induced by conditional expectations in such a setting. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-04 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/19426 Conde, Cristian Marcelo; Larotonda, Gabriel Andrés; Manifolds of semi-negative curvature; Wiley; Proceedings Of The London Mathematical Society; 100; 3; 4-2010; 670-704 0024-6115 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/19426 |
identifier_str_mv |
Conde, Cristian Marcelo; Larotonda, Gabriel Andrés; Manifolds of semi-negative curvature; Wiley; Proceedings Of The London Mathematical Society; 100; 3; 4-2010; 670-704 0024-6115 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/plms/pdp042/abstract info:eu-repo/semantics/altIdentifier/doi/10.1112/plms/pdp042 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf application/pdf |
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Wiley |
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Wiley |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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