I got the following problem: Let $F$ be a continously differentiable vector field with $div(F)=0$. We define an integral curve as a curve that is tangent to the vector field F.
Now let us take a curve C that is never tangent to F. When we look at the integral curves of F through C we get a surface, call it S.
Prove that the flux of F through every section of S is equal.
Any help? I tried to find a general parametrization to the surface F and compute the flux "by hand". I got that the flux is zero through every section but that seems odd, so I am probably mistaken. Plus, I haven't used that fact that the field is divergence free.
Please help :)