Anais da Academia Brasileira de Ciências
versão impressa ISSN 0001-3765
SANTOS FILHO, José R. dos e TAVARES, Joaquim. Injective mappings and solvable vector fields. An. Acad. Bras. Ciênc. [online]. 2010, vol.82, n.3, pp. 555-559. ISSN 0001-3765. http://dx.doi.org/10.1590/S0001-37652010000300002.
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.
Palavras-chave : fields; injectivity; mappings; solvability; vectors.