The distribution of Martinet is $\Delta=ker\omega$ with
$\omega=\Bbb dt-\frac{1}{2}y^{2}\Bbb dx$.
let $X=\partial x+\frac{1}{2}y^{2}\partial t$ and $Y=\partial y$
The curvature $2$-forme is: $\Omega=\Bbb d\omega$
so $\Omega=y\Bbb dx \wedge \Bbb dy$
I want to calculate $\Omega(X,Y)=y\Bbb dx \wedge \Bbb dy(X,Y)$.
I know how to calculate it in the Heisenberg case ($4\Bbb dx \wedge \Bbb dy$), but I don't know how in the Martinet case because of the unknown $y$.
should I fix the $y$, or is there something else I have to do?
Any help !!