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.
@article{1113247478,
author = {Cho, Sanghyun},
title = {Extension of CR structures on pseudoconvex CR manifolds with one degenerate eigenvalue},
journal = {Tohoku Math. J. (2)},
volume = {55},
number = {2},
year = {2003},
pages = { 321-360},
language = {en},
url = {http://dml.mathdoc.fr/item/1113247478}
}
Cho, Sanghyun. Extension of CR structures on pseudoconvex CR manifolds with one degenerate eigenvalue. Tohoku Math. J. (2), Tome 55 (2003) no. 2, pp. 321-360. http://gdmltest.u-ga.fr/item/1113247478/