On The Existence of Globally Solvable Vector Fields in Smooth Manifolds

Details On The Existence of Globally Solvable Vector Fields in Smooth Manifolds On The Existence of Globally Solvable Vector Fields in Smooth Manifolds

2008-06-20

arxiv.org/abs/0806.3451v5

Mathematics

Analysis of PDEs

10 pages

Scientific paper

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 $\mathrm{T M}$ such that its orbits becomes diffeomorphic to
an open convex set of $\mathbb{R}^{n}$, where $n$ is the orbit dimension.

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