Finitely curved orbits of complex polynomial vector fields

被引：1
|
作者：
Mafra, Albeta C. [1 ]
机构：
[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil
来源：
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS | 2007年 / 79卷 / 01期
关键词：
holomorphic foliations; polynomial vector fields; algebraic curves; finite total curvature;
D O I：
10.1590/S0001-37652007000100002
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C-2. We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C. C2 be a holomorphic curve which has finite total Gaussian curvature. Is C contained in an algebraic curve?
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页码：13 / 16
页数：4
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