Injective mappings and solvable vector fields

Anais da Academia Brasileira de Ciências

José R. Dos Santos Filho²  Joaquim Tavares¹ 

[1] ,Universidade Federal de São Carlos Departamento de Matemática São Carlos SP ,Brasil

关键词: fields;    injectivity;    mappings;    solvability;    vectors;    campos;    injetividade;    aplicações;    resolubilidade;    vetores;   

DOI  :  10.1590/S0001-37652010000300002

来源: SciELO

【 摘 要 】

We establish a sufficient condition for injectivity in a class of mappings defined on open connected subsets of Rn , for arbitrary n. The result relates solvability of the appropriate vector fields with injectivity of the mapping and extends a result proved by the first author for n < 3 . Furthermore, we extend the result to connected paracompact smooth oriented manifolds and show that the convexity condition imposes strong topological restrictions on the manifold.

【 授权许可】

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