Algebraic Classification of the Ricci Curvature Tensor and Spinor for Neutral Signature in Four Dimensions

Abstract

I apply the algebraic classification of self-adjoint endomorphisms of ${\mathbf{R}}^{2,2}$ 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.

arXiv comment67 pp, 2 tables; 2 figures

References in corpus (1)

• Spin coefficients for four-dimensional neutral metrics, and null geometry