Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold

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In this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher. It is demonstrated that these types of actions induce three complete holomorphic vector fields, one of which is periodic, and that there exists a particular relationship between them, given by...

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Detalles Bibliográficos
Autor: Ostos Cordero, Benito Leonardo
Formato: artículo
Fecha de Publicación:2024
Institución:Universidad Nacional de Trujillo
Repositorio:Revistas - Universidad Nacional de Trujillo
Lenguaje:español
OAI Identifier:oai:ojs.revistas.unitru.edu.pe:article/6159
Enlace del recurso:https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159
Nivel de acceso:acceso abierto
Materia:Campos vectoriales
corchete de Lie
acción holomorfa
conjunto singular
Vector fields
Lie bracket
holomorphic action
singular set
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spelling Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifoldFormas normales de campos vectoriales inducidos por acciones holomorfas del grupo SL(2,C) sobre una variedad complejaOstos Cordero, Benito LeonardoCampos vectorialescorchete de Lieacción holomorfaconjunto singularVector fieldsLie bracketholomorphic actionsingular setIn this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher. It is demonstrated that these types of actions induce three complete holomorphic vector fields, one of which is periodic, and that there exists a particular relationship between them, given by the Lie bracket, which generates a singular holomorphic foliation of codimension two. Subsequently, the types of singularities are classified, and the normal forms of these vector fields are obtained in a neighborhood of each singular point of the foliation.En este trabajo se estudian las acciones del grupo de Lie SL(2,C) sobre una variedad compleja de dimensión mayor o igual a tres. Se demuestra que este tipo de acciones induce tres campos vectoriales holomorfos completos, uno de los cuales es periódico, y que existe una relación particular entre ellos, dada por el corchete de Lie, que genera una foliación holomorfa singular de codimensión dos. Posteriormente, se clasifican los tipos de singularidades y se obtienen las formas normales de estos campos en una vecindad de cada punto singular de la foliación.National University of Trujillo - Academic Department of Mathematics2024-12-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159Selecciones Matemáticas; Vol. 11 No. 02 (2024): August - December; 285 - 302Selecciones Matemáticas; Vol. 11 Núm. 02 (2024): Agosto - Diciembre; 285 - 302Selecciones Matemáticas; v. 11 n. 02 (2024): Agosto - Dezembro; 285 - 3022411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUspahttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159/6262https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/61592024-12-28T04:55:24Z
dc.title.none.fl_str_mv Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
Formas normales de campos vectoriales inducidos por acciones holomorfas del grupo SL(2,C) sobre una variedad compleja
title Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
spellingShingle Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
Ostos Cordero, Benito Leonardo
Campos vectoriales
corchete de Lie
acción holomorfa
conjunto singular
Vector fields
Lie bracket
holomorphic action
singular set
title_short Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
title_full Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
title_fullStr Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
title_full_unstemmed Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
title_sort Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
dc.creator.none.fl_str_mv Ostos Cordero, Benito Leonardo
author Ostos Cordero, Benito Leonardo
author_facet Ostos Cordero, Benito Leonardo
author_role author
dc.subject.none.fl_str_mv Campos vectoriales
corchete de Lie
acción holomorfa
conjunto singular
Vector fields
Lie bracket
holomorphic action
singular set
topic Campos vectoriales
corchete de Lie
acción holomorfa
conjunto singular
Vector fields
Lie bracket
holomorphic action
singular set
description In this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher. It is demonstrated that these types of actions induce three complete holomorphic vector fields, one of which is periodic, and that there exists a particular relationship between them, given by the Lie bracket, which generates a singular holomorphic foliation of codimension two. Subsequently, the types of singularities are classified, and the normal forms of these vector fields are obtained in a neighborhood of each singular point of the foliation.
publishDate 2024
dc.date.none.fl_str_mv 2024-12-28
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159
url https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6159/6262
dc.rights.none.fl_str_mv https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
dc.source.none.fl_str_mv Selecciones Matemáticas; Vol. 11 No. 02 (2024): August - December; 285 - 302
Selecciones Matemáticas; Vol. 11 Núm. 02 (2024): Agosto - Diciembre; 285 - 302
Selecciones Matemáticas; v. 11 n. 02 (2024): Agosto - Dezembro; 285 - 302
2411-1783
reponame:Revistas - Universidad Nacional de Trujillo
instname:Universidad Nacional de Trujillo
instacron:UNITRU
instname_str Universidad Nacional de Trujillo
instacron_str UNITRU
institution UNITRU
reponame_str Revistas - Universidad Nacional de Trujillo
collection Revistas - Universidad Nacional de Trujillo
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 13.10263
Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold
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