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

Peter R Law

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arXiv · 1008.0444

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

Peter R Law

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Abstract

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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Peter R Law. 2010-08-03. Algebraic Classification of the Ricci Curvature Tensor and Spinor for Neutral Signature in Four Dimensions. https://arxiv.org/abs/1008.0444

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