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
Canonical name	LewyHypersurface
Date of creation	2013-03-22 14:49:01
Last modified on	2013-03-22 14:49:01
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	4
Author	jirka (4157)
Entry type	Example
Classification	msc 32V99