On weak holonomy - Alexandrov, Bogdan (MATHEMATICA SCANDINAVICA, 2005)
We prove that $SU(n)$ ($n \ge 3$) and $Sp(n)U(1)$ ($n \ge 2$) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group. In both cases the manifold is Kähler.