## Tohoku Mathematical Journal 2003 September SECOND SERIES VOL. 55, NO. 3

 Tohoku Math. J. 55 (2003), 321-360

Title EXTENSION OF CR STRUCTURES ON PSEUDOCONVEX CR MANIFOLDS WITH ONE DEGENERATE EIGENVALUE

Author Sanghyun Cho

(Received June 20, 2001, revised February 12, 2002)
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.

2000 Mathematics Subject Classification. Primary 32G05; Secondary 32GO7.

Key words and phrases. CR manifold, finite type, pseudoconvex.