Anais da Academia Brasileira de Ciências | |
On holomorphic one-forms transverse to closed hypersurfaces | |
Toshikazu Ito2  Bruno Scárdua1  | |
[1] ,Ryukoku University Department of Natural Science Kyoto,Japan | |
关键词: Holomorphic one-form; vector field; Euler-Poincaré characteristic; foliation; distribution; Um-forma holomorfa; campo de vetores; característica de Euler-Poincaré; folheação; distribuição; | |
DOI : 10.1590/S0001-37652003000300001 | |
来源: SciELO | |
【 摘 要 】
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.
【 授权许可】
CC BY
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO202103040000318ZK.pdf | 72KB | download |