Let M be a smooth manifold. Locally we can choose 1-forms \omega^{1},\omega^{2},...\omega^{n} whish span M^{*}_{q} for each q. Then are there vector fields X_{1}, X_{2}, ...,X_{n} with \omega^{i}(X_{j})=\delta^{i}_{j}? Here \delta^{i}_{j} is Kronecker delta.
By vector fields, I meant vector...