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

摘要

The topic of the paper is the study of germs of local holomorphisms $f$between $C^n$ and $C^{n'}$ such that $f(M)\subset M'$ and $df(T^cM)=T^cM'$ for$M\subset C^n$ and $M'\subset C^{n'}$ generic real-analytic CR submanifolds ofarbitrary codimensions. It is proved that for $M$ minimal and $M'$ finitelynondegenerate, such germs depend analytically on their jets. As a corollary, ananalytic structure on the set of all germs of this type is obtained.