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

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

2010-08-03

arxiv.org/abs/1008.0444v1

Mathematics

Differential Geometry

67 pp, 2 tables; 2 figures

Scientific paper

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.

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