On weak holonomy - Alexandrov, Bogdan (Mathematica Scandinavica, 2005)
We prove that SU(n) (n 3) and Sp(n)U(1) (n 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.