# Lewy hypersurface

The real hypersurface in $(z_{1},\ldots,z_{n})\in{\mathbb{C}}^{n}$ given by

 $\operatorname{Im}z_{n}=\sum_{j=1}^{n-1}\lvert z_{j}\rvert^{2}$

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 $\operatorname{Im}z_{n}=0$, but it is locally (not globally) biholomorphically equivalent to a unit sphere.

## References

• 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
Title Lewy hypersurface LewyHypersurface 2013-03-22 14:49:01 2013-03-22 14:49:01 jirka (4157) jirka (4157) 4 jirka (4157) Example msc 32V99