Injective mappings and solvable vector fields

Abstract

We establish a sufficient condition for injectivity in a class of mappings defined on open connected subsets of R n , 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.