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[parent] Lewy hypersurface (Example)

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

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

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.

Bibliography

1
M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. Real Submanifolds in Complex Space and Their Mappings, Princeton University Press, Princeton, New Jersey, 1999.



"Lewy hypersurface" is owned by jirka.
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Cross-references: unit sphere, hyperplane, biholomorphically equivalent, complex, dimension, real, real hypersurface
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This is version 1 of Lewy hypersurface, born on 2004-11-16.
Object id is 6478, canonical name is LewyHypersurface.
Accessed 1224 times total.

Classification:
AMS MSC: 32V99 (Several complex variables and analytic spaces :: CR manifolds :: Miscellaneous)
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