> Let M be a 3-manifold with a contact structure C , i.e., a nowhere-integrable hyperplane distribution.

>  I am trying to show that we can define locally (in a neighborhood Wx of each point x in M) a

>  form w , whose kernel is/defines the contact structure.

>     So, the idea is to define a 1-form whose kernel is precisely the hyperplane distribution.

>  My idea: for each x , we select first a basis B= {v1,v2} for the plane/hyperplane defined at x. We then

> extend the basis  B into a basis B' ={v1,v2,v3} for the tangent space at x, and we declare the form

>  w to satisfy w(v1)=w(v2)=0, and w(v3)=1  (every subspace is the kernel of  linear map ). Now,

>  I don't see what the obstruction is to defining a global contact structure. Any ideas?

> Thanks.