Proceedings of the Centre for Mathematics and its Applications

Degenerate holomorphic mappings of nondegenerate $CR$-manifolds

A. V. Isaev

Full-text: Open access

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

Source
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

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


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