Extension of CR structures on pseudoconvex CR manifolds with one degenerate eigenvalue

Abstract

Let $\bar M$ be a smoothly bounded orientable pseudoconvex CR manifold of finite type with at most one degenerate eigenvalue. Then we extend the given CR structure on $M$ to an integrable almost complex structure on the concave side of $M$. Therefore we may regard $M$ as the boundary of a complex manifold.