I am in $R^4$ in coordinates $x,y,z,t$. Can I extend an arbitrary 3-form defined only at points of the line $x=y=z=0$ to a closed 3-form in a neighbourhood of the line. In fact my question is only local, I do not need to have the whole line. My intuition says "yes", but I have no idea how to prove it, or where to look for similar extension theorems.
Added: Thanks to Ted Shifrin for his observation. That solves my problem. If I am, for instance, in Minkowski space, then the question can be transformed to divergenceless vector field. Then we extend all components $X^\mu(t)$ as constant with respect to x,y,z, except of, say the first one, which we make linear in $x$, like $X^1=x\, dX^4(t)/dt.$ Thanks