Two Exotic Holonomies in Dimension Four , Path Geometries , and Twistor Theory

Since its introduction by Élie Cartan, the holonomy of a connection has played an important role in differential geometry. One of the best known results concerning holonomy is Berger’s classification of the possible holonomies of Levi-Civita connections of Riemannian metrics. Since the appearance of Berger [1955], much work has been done to refine his list of possible Riemannian holonomies. See the recent works by Besse [1987] or Salamon [1989] for useful historical surveys and applications of holonomy to Riemannian and algebraic geometry.