It is known that near a strongly pseudoconvex point, the Levi rank at any boundary point is a constant, which is equal to $n$, the dimension of the domain.
I am looking for a bounded pseudoconvex domain $\Omega$ in $\mathbb{C}^{n}$ ($n>1$) such that there is a point $z_{0}\in\partial\Omega$ on the boundary so that $\partial\Omega$ has a constant Levi rank $k< n$ in a neighbourhood of $z_{0}$.
Thanks.