Finitely curved orbits of complex polynomial vector fields

Anais da Academia Brasileira de Ciências

Albetã C. Mafra¹ 

[1] ,Universidade Federal do Rio de Janeiro Instituto de Matemática Rio de Janeiro RJ ,Brasil

关键词: Holomorphic foliations;    polynomial vector fields;    algebraic curves;    finite total curvature;    Folheações holomorfas;    campos de vetores polinomiais;    curvas algébricas;    curvatura total finita;   

DOI  :  10.1590/S0001-37652007000100002

来源: SciELO

【 摘 要 】

This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². 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 Ì C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?

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