Complete system of finite order for the embeddings of pseudo-hermitian manifolds into CN+1

Let (M, V, theta) be a real analytic (2n+1)-dimensional pseudo-hermitian ma nifold with nondegenerate Levi form and F be a pseudo-hermitian embedding i nto Cn+1. We show under certain generic conditions that F satisfies a compl ete system of finite order. We use a method of prolongation of the tangenti al Cauchy-Riemann equations and pseudo-hermitian embedding equation. Thus i f F epsilon C-k(M) for sufficiently large k, F is real analytic. As a corol lary, if M is areal hypersurface in Cn+1, then F extends holomorphically to a neighborhood of M provided that F is sufficiently smooth.