Contact quasiconformal immersions

被引：0
作者：
Zorich V.A. [1 ]
机构：
[1] Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow
来源：
Proceedings of the Steklov Institute of Mathematics | 2006年 / 253卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Riemannian Manifold; STEKLOV Institute; Heisenberg Group; Quasiconformal Mapping; Contact Structure;
D O I：
10.1134/S0081543806020076
中图分类号：
学科分类号：
摘要：
Contact immersions of contact manifolds endowed with the associated Carnot-Carathéodory (CC) metric (for example, immersions of the Heisenberg group H3 ∼ ℝCC 3 in itself) are considered. It is assumed that the manifolds have the same dimension and the immersions are quasiconformal with respect to the CC metric. The main assertion is as follows: A quasiconformal immersion of the Heisenberg group in itself, just as a quasiconformal immersion of any contact manifold of conformally parabolic type in a simply connected contact manifold, is globally injective; i.e., such an immersion is an embedding, which, in addition, is surjective in the case of the Heisenberg group. Thus, the global homeomorphism theorem, which is well known in the space theory of quasiconformal mappings, also holds in the contact case. © Pleiades Publishing, Inc., 2006.
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页码：71 / 77
页数：6
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