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Geometric Interpretation of the Mixed Invariants of the Riemann Spinor

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GEOMETRIC INTERPRETATION OF THE MIXED INVARIANTS OF THE RIEMANN SPINOR Barry M Haddow ?School of Mathematics Trinity College Dublin 2IRELAND February 7,2008Abstract Mixed invariants are used to classify the Riemann spinor in the case of Einstein-Maxwell ?elds and perfect ?uids.In the Einstein-Maxwell case these mixed invariants provide information as to the relative orientation of the gravitational and electromagnetic principal null directions.Consideration of the perfect ?uid case leads to some

results about the behaviour of the Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.

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