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A Pontryagin class obstruction for purely electric and purely magnetic Weyl curvature tensors
Do all manifolds that admit Lorentzian metrics also admit such metrics that have a purely electric (PE) or purely magnetic (PM) Weyl curvature tensor? To (partially) answer this question, we show that for all algebraic curvature tensors on a $4k$-dimensional scalar product space that are even or odd
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