# Lewy hypersurface

The real hypersurface in $({z}_{1},\mathrm{\dots},{z}_{n})\in {\u2102}^{n}$ 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^{}.

## 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 |