%0 Journal Article %T On Parallel Sections of a Vector Bundle %A Richard Atkins %J Mathematics %D 2008 %I arXiv %X We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the bundle. The procedure is algebraic and rests upon the Frobenius Theorem. %U http://arxiv.org/abs/0804.1732v1