I met a statement saying:
The product structure $V=M\times\mathbb R$, with $M$ an orientable $3$-manifold, implies the existence of a global coframe (4 globally defined linearly independent 1-forms). The property does not extend to higher dimensions.
I can not prove this and do not know why this dimension 3 is special. Can someone give a proof and counterexamples?
Thank you.