Vanishing of top-degree Pontryagin class products obstructs purely electric or magnetic Weyl curvature on compact 4k-manifolds.
On curvature and characteristic classes of a Riemann manifold.Abh
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A Pontryagin class obstruction for purely electric and purely magnetic Weyl curvature tensors
Vanishing of top-degree Pontryagin class products obstructs purely electric or magnetic Weyl curvature on compact 4k-manifolds.