Why is  O（n;k）not connected，and it has four connection branches？
$O（n；k）=\{A\in GL(n+k，C)|A^{T}GA=G\}$
where 
$G=\begin{pmatrix}
1&&&&&\\
&\ddots& & & &\\
&&1&& &\\
&& &-1& &\\
&& & &\ddots &\\
&& & & &-1
\end{pmatrix}$，it has n 1 and k -1.