What is the exact relationship **hyper-complex** and **quaternionic Kahler manifolds**? From Wikipedia we get that hyper-Kahler manifolds are both hyper-complex and quaternionic Kahler. Thus, the two families have a non-empty intersection. But this is all I can conclude.

Moreover, **quaternionic projective space** is quaternionic Kahler, but is it also hyper-Kahler? Is it even hyper-complex?