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.