Curvature structure of self-dual 4-manifolds
  We show the existence of a modified Cliff(1,1) structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2). We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we prove some new results regarding (Jordan) Osserman manifolds. 
Novica Blazic, Peter Gilkey, Stana Nikcevic, and Iva Stavrov