is called the Lewy hypersurface. Note that this is a real hypersurface of realdimension. 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
, but it is locally (not globally) biholomorphically equivalent to a unit sphere.
M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. Real Submanifolds in Complex Space and Their Mappings, Princeton University Press, Princeton, New Jersey, 1999.