On holomorphic one-forms transverse to closed hypersurfaces
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| Format: | Artículo científico |
| Sprache: | en |
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Academia Brasileira de Ciências
2003
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| _version_ | 1876424356160077824 |
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| author | Toshikazu Ito |
| author_facet | Toshikazu Ito |
| contents | On holomorphic one-forms transverse to closed hypersurfaces Toshikazu Ito Bruno Scárdua Multidisciplinaria (Ciencias Naturales y Exactas) form Euler foliation vector field distribution In this note we announce some achievements in the study of holomorphic distributions admittingtransverse closed real hypersurfaces. We consider a domain with smooth boundary in the complexaffine space of dimension two or greater. Assume that the domain satisfies some cohomologytriviality hypothesis (for instance, if the domain is a ball). We prove that if a holomorphic oneform in a neighborhood of the domain is such that the corresponding holomorphic distributionis transverse to the boundary of the domain then the Euler-Poincaré-Hopf characteristic of thedomain 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 oneholomorphic foliations transverse to spheres. 2003 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32775301 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.75 |
| format | Artículo científico |
| id | redalyc_32775301 |
| institution | Redalyc |
| language | en |
| publishDate | 2003 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | On holomorphic one-forms transverse to closed hypersurfaces Toshikazu Ito Multidisciplinaria (Ciencias Naturales y Exactas) form Euler foliation vector field distribution On holomorphic one-forms transverse to closed hypersurfaces Toshikazu Ito Bruno Scárdua Multidisciplinaria (Ciencias Naturales y Exactas) form Euler foliation vector field distribution In this note we announce some achievements in the study of holomorphic distributions admittingtransverse closed real hypersurfaces. We consider a domain with smooth boundary in the complexaffine space of dimension two or greater. Assume that the domain satisfies some cohomologytriviality hypothesis (for instance, if the domain is a ball). We prove that if a holomorphic oneform in a neighborhood of the domain is such that the corresponding holomorphic distributionis transverse to the boundary of the domain then the Euler-Poincaré-Hopf characteristic of thedomain 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 oneholomorphic foliations transverse to spheres. 2003 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32775301 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.3 Vol.75 |
| title | On holomorphic one-forms transverse to closed hypersurfaces |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) form Euler foliation vector field distribution |
| url | https://www.redalyc.org/articulo.oa?id=32775301 |