The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday
- Autores
- Olmos, Carlos; Reggiani, Silvio Nicolás
- Año de publicación
- 2012
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use any classification (not even that of transitive isometric actions on the sphere or the list of rank one symmetric spaces). This result was independently proved, by using an algebraic approach, by Paul- Andy Nagy. We apply this theorem to prove that the canonical connection of a compact naturally reductive space is unique, provided the space does not split o? locally, a sphere or a compact Lie group with a bi-invariant metric. From this it follows easily how to obtain the full isometry group of a naturally reductive space. This generalizes known classification results of Onishchick, for normal homogeneous spaces with simple group of isometries, and Shankar, for homogeneous spaces of positive curvature. This also answers a question posed by J. Wolf and Wang-Ziller. Namely, to explain why the presentation group of an isotropy irreducible space, strongly or not, cannot be enlarged (except for spheres, or for compact simple Lie groups with a bi-invariant metric).
Fil: Olmos, Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina - Materia
-
HOLONOMY
SKEW-TORSION
NATURALLY REDUCTIVE
ISOMETRY GROUP - 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:11336/195607
Ver los metadatos del registro completo
id |
CONICETDig_d04905af0f1044dcc09a7607bd8b17c3 |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/195607 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
network_name_str |
CONICET Digital (CONICET) |
spelling |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthdayOlmos, CarlosReggiani, Silvio NicolásHOLONOMYSKEW-TORSIONNATURALLY REDUCTIVEISOMETRY GROUPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use any classification (not even that of transitive isometric actions on the sphere or the list of rank one symmetric spaces). This result was independently proved, by using an algebraic approach, by Paul- Andy Nagy. We apply this theorem to prove that the canonical connection of a compact naturally reductive space is unique, provided the space does not split o? locally, a sphere or a compact Lie group with a bi-invariant metric. From this it follows easily how to obtain the full isometry group of a naturally reductive space. This generalizes known classification results of Onishchick, for normal homogeneous spaces with simple group of isometries, and Shankar, for homogeneous spaces of positive curvature. This also answers a question posed by J. Wolf and Wang-Ziller. Namely, to explain why the presentation group of an isotropy irreducible space, strongly or not, cannot be enlarged (except for spheres, or for compact simple Lie groups with a bi-invariant metric).Fil: Olmos, Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaDe Gruyter2012-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/195607Olmos, Carlos; Reggiani, Silvio Nicolás; The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday; De Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 664; 3-2012; 29-530075-4102CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/CRELLE.2011.100info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/document/doi/10.1515/CRELLE.2011.100/htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:46:09Zoai:ri.conicet.gov.ar:11336/195607instacron: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 10:46:09.476CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
title |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
spellingShingle |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday Olmos, Carlos HOLONOMY SKEW-TORSION NATURALLY REDUCTIVE ISOMETRY GROUP |
title_short |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
title_full |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
title_fullStr |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
title_full_unstemmed |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
title_sort |
The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday |
dc.creator.none.fl_str_mv |
Olmos, Carlos Reggiani, Silvio Nicolás |
author |
Olmos, Carlos |
author_facet |
Olmos, Carlos Reggiani, Silvio Nicolás |
author_role |
author |
author2 |
Reggiani, Silvio Nicolás |
author2_role |
author |
dc.subject.none.fl_str_mv |
HOLONOMY SKEW-TORSION NATURALLY REDUCTIVE ISOMETRY GROUP |
topic |
HOLONOMY SKEW-TORSION NATURALLY REDUCTIVE ISOMETRY GROUP |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use any classification (not even that of transitive isometric actions on the sphere or the list of rank one symmetric spaces). This result was independently proved, by using an algebraic approach, by Paul- Andy Nagy. We apply this theorem to prove that the canonical connection of a compact naturally reductive space is unique, provided the space does not split o? locally, a sphere or a compact Lie group with a bi-invariant metric. From this it follows easily how to obtain the full isometry group of a naturally reductive space. This generalizes known classification results of Onishchick, for normal homogeneous spaces with simple group of isometries, and Shankar, for homogeneous spaces of positive curvature. This also answers a question posed by J. Wolf and Wang-Ziller. Namely, to explain why the presentation group of an isotropy irreducible space, strongly or not, cannot be enlarged (except for spheres, or for compact simple Lie groups with a bi-invariant metric). Fil: Olmos, Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina |
description |
We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use any classification (not even that of transitive isometric actions on the sphere or the list of rank one symmetric spaces). This result was independently proved, by using an algebraic approach, by Paul- Andy Nagy. We apply this theorem to prove that the canonical connection of a compact naturally reductive space is unique, provided the space does not split o? locally, a sphere or a compact Lie group with a bi-invariant metric. From this it follows easily how to obtain the full isometry group of a naturally reductive space. This generalizes known classification results of Onishchick, for normal homogeneous spaces with simple group of isometries, and Shankar, for homogeneous spaces of positive curvature. This also answers a question posed by J. Wolf and Wang-Ziller. Namely, to explain why the presentation group of an isotropy irreducible space, strongly or not, cannot be enlarged (except for spheres, or for compact simple Lie groups with a bi-invariant metric). |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-03 |
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/11336/195607 Olmos, Carlos; Reggiani, Silvio Nicolás; The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday; De Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 664; 3-2012; 29-53 0075-4102 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/195607 |
identifier_str_mv |
Olmos, Carlos; Reggiani, Silvio Nicolás; The skew-torsion holonomy theorem and naturally reductive spaces: To Isabel Dotti and Roberto Miatello on the occasion of their birthday; De Gruyter; Journal Fur Die Reine Und Angewandte Mathematik; 664; 3-2012; 29-53 0075-4102 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1515/CRELLE.2011.100 info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/document/doi/10.1515/CRELLE.2011.100/html |
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 |
dc.publisher.none.fl_str_mv |
De Gruyter |
publisher.none.fl_str_mv |
De Gruyter |
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 |
_version_ |
1844614502630293504 |
score |
13.070432 |