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The Scientific World Journal
Volume 2014, Article ID 930571, 9 pages
http://dx.doi.org/10.1155/2014/930571
Research Article

1-Quasiconformal Mappings and CR Mappings on Goursat Groups

Department of Mathematics, Linyi University, Linyi, Shandong 276005, China

Received 27 February 2014; Accepted 2 April 2014; Published 24 April 2014

Academic Editor: Dachun Yang

Copyright © 2014 Qing Yan Wu and Zun Wei Fu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show that 1-quasiconformal mappings on Goursat groups are CR or anti-CR mappings. This can reduce the determination of 1-quasiconformal mappings to the determination of CR automorphisms of CR manifolds, which is a fundamental problem in the theory of several complex variables.