I'm writing because of a problem in constructiong the foliation associated to a differential one-form.
Explicitely I have the following differential one-form $\theta$ on Minkowski spacetime $\mathcal{M}$:
$$ \theta=\frac{1}{\sqrt{(x^{1})^{2}-(x^{0})^{2}}}\left(x^{1}dx^{0}-x^{0}dx^{1}\right) $$ and I want to find the foliation associated to it.
The differential one-form $\theta$ is integrable, in the sense of Frobenius theorem, i.e. $\theta\wedge d\theta=0$.
I'm sorry but I can not provide any more insights because I'm not very confident with foliations.
In the concrete I want to find the explicit form of the leaves of the foliation.
Thank You.