On holomorphic one-forms transverse to closed hypersurfaces

Detalhes bibliográficos
Autor(a) principal: Ito,Toshikazu
Data de Publicação: 2003
Outros Autores: Scárdua,Bruno
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652003000300001
Resumo: In this note we announce some achievements in the study of holomorphic distributions admitting transverse closed real hypersurfaces. We consider a domain with smooth boundary in the complex affine space of dimension two or greater. Assume that the domain satisfies some cohomology triviality hypothesis (for instance, if the domain is a ball). We prove that if a holomorphic one form in a neighborhood of the domain is such that the corresponding holomorphic distribution is transverse to the boundary of the domain then the Euler-Poincaré-Hopf characteristic of the domain is equal to the sum of indexes of the one-form at its singular points inside the domain. This result has several consequences and applies, for instance, to the study of codimension one holomorphic foliations transverse to spheres.
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spelling On holomorphic one-forms transverse to closed hypersurfacesHolomorphic one-formvector fieldEuler-Poincaré characteristicfoliationdistributionIn this note we announce some achievements in the study of holomorphic distributions admitting transverse closed real hypersurfaces. We consider a domain with smooth boundary in the complex affine space of dimension two or greater. Assume that the domain satisfies some cohomology triviality hypothesis (for instance, if the domain is a ball). We prove that if a holomorphic one form in a neighborhood of the domain is such that the corresponding holomorphic distribution is transverse to the boundary of the domain then the Euler-Poincaré-Hopf characteristic of the domain is equal to the sum of indexes of the one-form at its singular points inside the domain. This result has several consequences and applies, for instance, to the study of codimension one holomorphic foliations transverse to spheres.Academia Brasileira de Ciências2003-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652003000300001Anais da Academia Brasileira de Ciências v.75 n.3 2003reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652003000300001info:eu-repo/semantics/openAccessIto,ToshikazuScárdua,Brunoeng2003-08-25T00:00:00Zoai:scielo:S0001-37652003000300001Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2003-08-25T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv On holomorphic one-forms transverse to closed hypersurfaces
title On holomorphic one-forms transverse to closed hypersurfaces
spellingShingle On holomorphic one-forms transverse to closed hypersurfaces
Ito,Toshikazu
Holomorphic one-form
vector field
Euler-Poincaré characteristic
foliation
distribution
title_short On holomorphic one-forms transverse to closed hypersurfaces
title_full On holomorphic one-forms transverse to closed hypersurfaces
title_fullStr On holomorphic one-forms transverse to closed hypersurfaces
title_full_unstemmed On holomorphic one-forms transverse to closed hypersurfaces
title_sort On holomorphic one-forms transverse to closed hypersurfaces
author Ito,Toshikazu
author_facet Ito,Toshikazu
Scárdua,Bruno
author_role author
author2 Scárdua,Bruno
author2_role author
dc.contributor.author.fl_str_mv Ito,Toshikazu
Scárdua,Bruno
dc.subject.por.fl_str_mv Holomorphic one-form
vector field
Euler-Poincaré characteristic
foliation
distribution
topic Holomorphic one-form
vector field
Euler-Poincaré characteristic
foliation
distribution
description In this note we announce some achievements in the study of holomorphic distributions admitting transverse closed real hypersurfaces. We consider a domain with smooth boundary in the complex affine space of dimension two or greater. Assume that the domain satisfies some cohomology triviality hypothesis (for instance, if the domain is a ball). We prove that if a holomorphic one form in a neighborhood of the domain is such that the corresponding holomorphic distribution is transverse to the boundary of the domain then the Euler-Poincaré-Hopf characteristic of the domain is equal to the sum of indexes of the one-form at its singular points inside the domain. This result has several consequences and applies, for instance, to the study of codimension one holomorphic foliations transverse to spheres.
publishDate 2003
dc.date.none.fl_str_mv 2003-09-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652003000300001
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652003000300001
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652003000300001
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.75 n.3 2003
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
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instname_str Academia Brasileira de Ciências (ABC)
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institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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