A PARAMETRIZED DE RHAM DECOMPOSITION THEOREM FOR CR MANIFOLDS

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 is an element of N. Let M be a totality of N and M(p) with moving p in N. Assume that M and (M) over tilde (with a same structure as M) are CR equivalent and that N and (N) over tilde are also CR equivalent. Then we prove that, for any p is an element of N, there exists (p) over tilde is an element of (N) over tilde such that M(p) is CR equivalent to (M) over tilde((p) over tilde).