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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19426

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spelling 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
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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