Lewy hypersurface

The real hypersurface in $(z_1,\mathrm{\dots },z_n)\in {ℂ}^n$ given by

$$\mathrm{Im}{z}_n=\sum _{j=1}^{n-1}{|z_j|}^2$$

is called the Lewy hypersurface. Note that this is a real hypersurface of real dimension $2n-1$. This is an example of a non-trivial real hypersurface in complex space. For example it is not biholomorphically equivalent to the hyperplane defined by $\mathrm{Im}{z}_n=0$, but it is locally (not globally) biholomorphically equivalent to a unit sphere.