I'm studying differential forms and have two questions about them.
1) I'm stuck with the following task given by my teacher: give an example of closed but not exact 1-form defined on $\Omega = \Bbb{R}^3 \setminus \{(at, bt, (a + b)t): t \in \Bbb{R}\}$ where both $a$ and $b$ are fixed.
I already know the proposition that differential 1-form $\omega$ is not exact if there are such closed curve $\Gamma: \oint_{\Gamma}\omega \neq 0$. But how can i find such differential form ?
2) And also I want to know if there any closed but not exact 2-forms on $\Omega$?