%0 Journal Article
%T On the Poincar¡äe-Hopf Index Theorem for the complex case
%A Toshikazu ItoBruno Sc¡äardua
%J The Open Mathematics Journal
%D 2008
%I 
%R 10.2174/1874117400801010001]
%X In this paper we consider holomorphic vector fields and holomorphic one-forms defining distributions which are transverse to the boundary of a regular domain on a complex manifold or on the complex affine space. In both cases we prove that, under a natural extensibility topological hypothesis, the Euler-Poincar¡äe-Hopf characteristic of the domain is equal to the sum of indexes of the complex vector field or complex one-form at its singular points inside the domain.
%U http://www.benthamscience.com/open/tomatj/articles/V001/1TOMATJ.htm