The question is to put a condition on the 2x2 matrix $H$
which is in the form
$$ \left( \begin{matrix} z & w\\ -\bar{w} & \bar{z}\\ \end{matrix} \right) $$
where z and w are complex numbers.
such that with that condition you get a cylinder (ie $S^1$ x [a,b])
The answer is supposed to be
$$ \left( \begin{matrix} e^{i\theta} & c\\ -c & e^{-i\theta}\\ \end{matrix} \right) $$
Where $c \in R$
And I have no clue why,