English

Germs of local automorphisms of real-analytic CR structures and analytic dependence on $k$-jets

Complex Variables 2007-05-23 v1

Abstract

The topic of the paper is the study of germs of local holomorphisms ff between CnC^n and CnC^{n'} such that f(M)Mf(M)\subset M' and df(TcM)=TcMdf(T^cM)=T^cM' for MCnM\subset C^n and MCnM'\subset C^{n'} generic real-analytic CR submanifolds of arbitrary codimensions. It is proved that for MM minimal and MM' finitely nondegenerate, such germs depend analytically on their jets. As a corollary, an analytic structure on the set of all germs of this type is obtained.

Keywords

Cite

@article{arxiv.math/9801041,
  title  = {Germs of local automorphisms of real-analytic CR structures and analytic dependence on $k$-jets},
  author = {Dmitri Zaitsev},
  journal= {arXiv preprint arXiv:math/9801041},
  year   = {2007}
}

Comments

17 pages