Riemannian, Symplectic and Weak Holonomy

Much of the early work of Alfred Gray was concerned with the investigation of Riemannian manifolds with special holonomy, one of the most vivid fields of Riemannian geometry in the 1960s and the following decades. It is the purpose of the present article to give a brief summary and an appreciation of Gray's contributions in this area on the one hand, and on the other hand to describe some of the more recent developments in the theory of non-Riemannian or,more specifically, symplectic holonomy groups. Namely, we show that the Merkulov twistor space of a connection on a symplectic manifold M whose holonomy group is irreducible and properly contained in Sp(V) consists of maximal totally geodesic Lagrangian submanifolds of M.