As described e.g. here the following is the standard contact form on $\mathbb R^{2n+1}$:
$$ \omega = dz + \sum_{k=1}^n x_k dy_k$$
Similarly, the following is the standard contact form on $S^{2n+1}$:
$$ \beta = \sum_{k=1}^{n+1} x_k dy_k - y_k dx_k$$
These are two examples of contact forms. Some contact forms are defined globally, everywhere on a given manifold. Some are not. At least that's what I understand so far.
My question is:
How can I determine whether a given contact form on a manifold is globally defined on that manifold or only locally?