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

الأصل · EN

The topic of the paper is the study of germs of local holomorphisms f between Cⁿ and Cⁿ' such that f(M)⊂ M' and df(TᶜM)=TᶜM' for M⊂ Cⁿ and M'⊂ Cⁿ' generic real-analytic CR submanifolds of arbitrary codimensions. It is proved that for M minimal and M' 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.