I'm looking for an introduction to holomorphic foliations and foliations of complex manifolds.


Any little helps, but I'm particularily interested in problems of the type where we have a hermitian manifold $(X,h)$ (not necessarily compact) and a foliation $\mathcal F$ of $X$, such that the restriction of $h$ to any leaf of the foliation is Kahler. Anything that could help to describe existence of such foliations, or consequences of their existence, would be greatly appreciated. But, to begin with:


Is there any general introduction to the theory of foliations on complex manifolds?



References for holomorphic foliations
As far as I can remember right now, the great general introduction to the theory of holomorphic foliations is yet to be written. Anyway let me mention some of the books that
I know and which you may find useful. Let me warn you that none of them address your specific question.


1. Brunella - Birational geometry of foliations
2. Suwa - Indices of vector fields and residues of holomorphic foliations
3. Gomez-Mont, Bobadilla - Sistemas Dinamicos Holomorfos en Superficies ( in Spanish )
4. Loray - [Pseudo-groupe d'une singularité de feuilletage holomorphe en dimension deux](http://hal.archives-ouvertes.fr/ccsd-00016434) (in French )
5. Camacho, Sad - Pontos singulares de equações diferenciais analiticas ( in Portuguese )
6. Lins Neto, Scárdua - Folheações algébricas complexas ( in Portuguese )
7. Lins Neto - Componentes irredutíveis dos espaços de folheações ( in Portuguese )


Let me also mention that F. Touzet recently studied foliations admitting a transversal Kähler metric in [this paper](http://perso.univ-rennes1.fr/frederic.touzet/frieman.pdf).


