Connections with exotic holonomy
In 1955, Berger (Ber) partially classified the possible irreducible holonomy representations of torsion free connections on the tangent bundle of a manifold. However, it was shown by Bryant (Br2) that Berger's list is incomplete. Connections whose holonomy is not contained on Berger's list are called exotic. We investigate examples of a certain 4-dimensional exotic holonomy representation of $Sl(2, \IR).$ We show that connections with this holonomy are never complete, give explicit descriptions of these connections on an open dense set and compute their group of symmetry. Finally, we give strong restrictions for their existence on compact manifolds.
Schwachhofer, Lorenz Johannes, "Connections with exotic holonomy" (1992). Dissertations available from ProQuest. AAI9235201.