I apply the algebraic classification of self-adjoint endomorphisms of ${ \bf R}^{ 2,2}$ provided by their Jordan canonical form to the Ricci curvature tensor of four-dimensional neutral manifolds and relate this classification to an algebraic classification of the Ricci curvature spinor. These results parallel similar results well known in four-dimensional Lorentzian geometry. The classification is summarized in Table 2 at the end of the paper.
Categories: math.DG math-ph math.MP