  We show that a complex projective manifold X which satisfies the Gromov's
h-principle is `special', and raise some questions about the reverse
implication, the extension to the quasi-K\" ahler case, and the relationships
of these properties to the `Oka' property. The guiding principle is that the
existence of many Stein manifolds which have degenerate Kobayashi pseudometric
gives strong obstructions to the complex hyperbolicity of X satisfying the
h-principle.
