Let $\mathcal{M}$ be a smooth manifold of dimension $m<+\infty$. Let $\theta$ be a nowhere vanishing (non-singular) differential one-form on $\mathcal{M}$ such that $\theta\wedge d\theta=0$. According to Frobenious' theorem, the kernel of $\theta$ is an involutive distribution and thus generates a codimension-one foliation $\mathcal{F}$ of $\mathcal{M}$.
The foliation $\mathcal{F}$ is defined to be regular if all of its leaves are regular submanifolds of $\mathcal{M}$. I would like to know if there are some conditions on $\theta$ assuring that the foliation $\mathcal{F}$ is regular without the need to explicitely find the leaves of $\mathcal{F}$.
Thamk You