A Poincare-Hopf-type theorem for holomorphic one-forms

被引：6

作者：

Ito, T

Scárdua, B

机构：

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil

[2] Ryukoku Univ, Dept Nat Sci, Fushimi Ku, Kyoto 612, Japan

来源：

TOPOLOGY | 2005年 / 44卷 / 01期

关键词：

holomorphic distribution; holomorphic foliation; foliation transverse to sphere;

D O I：

10.1016/j.top.2004.03.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if a holomorphic one-form Omega in a neighborhood of a closed euclidian ball B-2n subset of C-n, in the n-dimensional complex affine space, defines a distribution transverse to the boundary sphere S2n-1 = partial derivativeB(2n), then n is even and Omega admits a sole singularity q is an element of B-2n. Moreover, this singularity is simple. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：73 / 84

页数：12