Normal Holonomy of CR-submanifolds

Autores
Vittone, Francisco; Di Scala, Antonio J.
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.
Fil: Vittone, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Di Scala, Antonio J.. Politecnico di Torino; Italia
Materia
NORMAL HOLONOMY
CR-SUBMANIFOLDS
NORMAL CONNECTION
S-REPRESENTATION
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:11336/54857
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Normal Holonomy of CR-submanifoldsVittone, FranciscoDi Scala, Antonio J.NORMAL HOLONOMYCR-SUBMANIFOLDSNORMAL CONNECTIONS-REPRESENTATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.Fil: Vittone, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Di Scala, Antonio J.. Politecnico di Torino; ItaliaOsaka University. Departments of Mathematics2017-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/54857Vittone, Francisco; Di Scala, Antonio J.; Normal Holonomy of CR-submanifolds; Osaka University. Departments of Mathematics; Osaka Journal of Mathematics; 54; 1; 1-2017; 17-350030-6126CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.5778info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.ojm/1488531782info:eu-repo/semantics/altIdentifier/url/http://www.math.sci.osaka-u.ac.jp/ojm/contents.html#54-1info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:37:53Zoai:ri.conicet.gov.ar:11336/54857instacron: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 09:37:53.905CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Normal Holonomy of CR-submanifolds
title Normal Holonomy of CR-submanifolds
spellingShingle Normal Holonomy of CR-submanifolds
Vittone, Francisco
NORMAL HOLONOMY
CR-SUBMANIFOLDS
NORMAL CONNECTION
S-REPRESENTATION
title_short Normal Holonomy of CR-submanifolds
title_full Normal Holonomy of CR-submanifolds
title_fullStr Normal Holonomy of CR-submanifolds
title_full_unstemmed Normal Holonomy of CR-submanifolds
title_sort Normal Holonomy of CR-submanifolds
dc.creator.none.fl_str_mv Vittone, Francisco
Di Scala, Antonio J.
author Vittone, Francisco
author_facet Vittone, Francisco
Di Scala, Antonio J.
author_role author
author2 Di Scala, Antonio J.
author2_role author
dc.subject.none.fl_str_mv NORMAL HOLONOMY
CR-SUBMANIFOLDS
NORMAL CONNECTION
S-REPRESENTATION
topic NORMAL HOLONOMY
CR-SUBMANIFOLDS
NORMAL CONNECTION
S-REPRESENTATION
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 study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.
Fil: Vittone, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Di Scala, Antonio J.. Politecnico di Torino; Italia
description We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/54857
Vittone, Francisco; Di Scala, Antonio J.; Normal Holonomy of CR-submanifolds; Osaka University. Departments of Mathematics; Osaka Journal of Mathematics; 54; 1; 1-2017; 17-35
0030-6126
CONICET Digital
CONICET
url http://hdl.handle.net/11336/54857
identifier_str_mv Vittone, Francisco; Di Scala, Antonio J.; Normal Holonomy of CR-submanifolds; Osaka University. Departments of Mathematics; Osaka Journal of Mathematics; 54; 1; 1-2017; 17-35
0030-6126
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.5778
info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.ojm/1488531782
info:eu-repo/semantics/altIdentifier/url/http://www.math.sci.osaka-u.ac.jp/ojm/contents.html#54-1
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 Osaka University. Departments of Mathematics
publisher.none.fl_str_mv Osaka University. Departments of Mathematics
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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score 13.070432

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