On The Existence of Globally Solvable Vector Fields in Smooth Manifolds

Abstract

Let $(\mathrm{M},{\omega }_0)$ be a connected paracompact smooth oriented manifold. We establish a necessary and sufficient conditions on Lie subalgebra $\mathfrak{a}$ of $\mathrm{TM}$ such that its orbits becomes diffeomorphic to an open convex set of ${\mathbb{R}}^n$, where $n$ is the orbit dimension.

10 pages