## Proceedings of the Centre for Mathematics and its Applications

### Degenerate holomorphic mappings of nondegenerate $CR$-manifolds

A. V. Isaev

#### Abstract

We announce the following result: the Jacobian of a locally defined holomorphic mapping between two real-analytic $CR$-manifolds $M_1$ and $M_2$ in $\mathbb{C}^N$ where $M_1$ has a nondegenerate Levi form and satisfies a certain rigidity c~ndition, is identically zero, if it is zero at one point on $M_1$. We also give a description of the image of the mapping in terms of the geometry of $M_2$.

#### Article information

Dates
First available in Project Euclid: 18 November 2014

Isaev, A. V. Degenerate holomorphic mappings of nondegenerate $CR$-manifolds. Miniconferences on Analysis and Applications, 99--106, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1994. https://projecteuclid.org/euclid.pcma/1416323444