On holomorphic one-forms transverse to closed hypersurfaces

Anais da Academia Brasileira de Ciências

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