A parametrized de Rham decomposition theorem for CR manifolds

Abstract

The CR equivalence problem between CR manifolds with slice structure is studied. Let N be a connected holomorphically nondegenerate real analytic hypersurface and M(p) a finitely nondegenerate real analytic hypersurface parametrized by p ∈ N . Let M be a totality of N and M(p) with moving p in N . Assume that M and M (with a same structure as M) are CR equivalent and that N and N are also CR equivalent. Then we prove that, for any p ∈ N , there exists p ∈ N such that M(p) is CR equivalent to M( p).