## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Miniconference on Analysis and Applications. Gaven Martin and Bevan Thompson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 33. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1994), 99 - 106

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416323444

**Mathematical Reviews number (MathSciNet)**

MR1332506

**Zentralblatt MATH identifier**

0843.32010

#### Citation

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